The agricultural production space,as where and how much each agricultural product grows,plays a vital role in meeting the increasing and diverse food demands.Previous studies on agricultural production patterns have p...The agricultural production space,as where and how much each agricultural product grows,plays a vital role in meeting the increasing and diverse food demands.Previous studies on agricultural production patterns have predominantly centered on individual or specific crop types,using methods such as remote sensing or statistical metrological analysis.In this study,we characterize the agricultural production space(APS)by bipartite network connecting agricultural products and provinces,to reveal the relatedness between diverse agricultural products and the spatiotemporal characteristic of provincial production capabilities in China.The results show that core products are cereal,pork,melon,and pome fruit;meanwhile the milk,grape,and fiber crop show an upward trend in centrality,which is in line with diet structure changes in China over the past decades.The little changes in community components and structures of agricultural products and provinces reveal that agricultural production patterns in China are relatively stable.Additionally,identified provincial communities closely resemble China's agricultural natural zones.Furthermore,the observed growth in production capabilities in North and Northeast China implies their potential focus areas for future agricultural production.Despite the superior production capa-bilities of southern provinces,recent years have witnessed a notable decline,warranting special attentions.The findings provide a comprehensive perspective for understanding the complex relationship of agricultural prod-ucts'relatedness,production capabilities and production patterns,which serve as a reference for the agricultural spatial optimization and agricultural sustainable development.展开更多
For analytic functions u,ψin the unit disk D in the complex plane and an analytic self-mapφof D,we describe in this paper the boundedness and compactness of product type operators T_(u,ψ,φ)f(z)=u(z)f(φ(z))+ψ(z)f...For analytic functions u,ψin the unit disk D in the complex plane and an analytic self-mapφof D,we describe in this paper the boundedness and compactness of product type operators T_(u,ψ,φ)f(z)=u(z)f(φ(z))+ψ(z)f'(φ(z)),z∈D,acting between weighted Bergman spaces induced by a doubling weight and a Bloch type space with a radial weight.展开更多
Taking Zhaoyu Historical City in Qixian County as an example,this paper explores the production process of tourism space in Zhaoyu Historical City in the context of consumption,based on Lefebvre's triadic dialecti...Taking Zhaoyu Historical City in Qixian County as an example,this paper explores the production process of tourism space in Zhaoyu Historical City in the context of consumption,based on Lefebvre's triadic dialectic theory.The study reveals that,driven by the development of tourism,subjects such as the government and planners possess absolute dominance over spatial representations,while residents demonstrate receptive and adaptive action strategies and social relations are reproduced,presenting a harmonious state.Further exploring the tourism community in the environmental performance of the subject of action,social relations,consumption demand,daily life practice,cultural capital,etc.,the daily life practice of the tourism community has transcended the original logic of tourism spatial production and has a certain extension.The mechanism analysis in this paper can help guide the healthy development of tourism space in the neighboring historical cities or communities and achieve the dual purpose of promoting the economic development of the community and heritage protection.展开更多
The contradiction between the shortage of land for agriculture due to rapid expansion of industrialization and urbanization and increasing population pressure is projected to impose great threats to future food securi...The contradiction between the shortage of land for agriculture due to rapid expansion of industrialization and urbanization and increasing population pressure is projected to impose great threats to future food security.Agricultural land suitability evaluation is an effective approach to improve the utilization of land resources for crop production and thus enhance the capacity of food provision.In this study, we evaluated the land suitability for agriculture of the production space in the Taihang Mountains by three steps: establishing indicator system, determining weights for indicators, and constructing a fuzzy matter-element model to assess the grades of suitability.Results showed that the land suitability had a significant linear correlation with potential crop yields, indicating our evaluation was effective to predict crop production.The spatial pattern of land suitability for crop production demonstrated that land with higher suitability was generally located in piedmont plains and basins, while land with lower suitability was mostly situated in mountainous areas.The area of highly, moderately, marginally suitable and unsuitable land for agriculture was 32.13%, 28.58%, 37.49% and 1.80% of the production space, respectively.However, the correlation degree analysis indicated that the requirements of these four suitability grades were currently not satisfied but could be potentially fulfilled.In terms of indicator weights, soil properties were much more important than topography and location conditions to influence the grades of suitability.Among all indicators, slope, soil organic matter, soil texture and soil depth were the most influential factors, so slope farming prevention and organic fertilization were most likely to improve land suitability for agriculture.Compared the outputs of our land suitability evaluation model with the distribution of the existing croplands, we found that about 66.52% of marginally suitable and 54.55% of unsuitable land for agriculture were currently used for croplands.Therefore, de-farming policy should be implemented in areas of these two suitability grades.In contrast, cropland expansion was encouraged in the land that was highly or moderately suitable for agriculture.Our evaluation of agricultural land suitability is beneficial for future land use planning and decision-making in the Taihang Mountains.展开更多
For a long time,it has been argued that the theories and practices devoted to urban planning and management should conform to the fundamental role of planning policies in the production of urban space,but not merely t...For a long time,it has been argued that the theories and practices devoted to urban planning and management should conform to the fundamental role of planning policies in the production of urban space,but not merely the spatial distribution of the produced services.Towards this wider connotation,this study introduces the notion of Railwayscape,grounded on the theory of‘The Production of Space’,to examine the role of railway station districts as catalysts of urban development through the social production of urban space.The present research sets out to establish the notion of Railwayscape and apply it in a railway heritage,i.e.,the Darjeeling Himalayan Railway(DHR)and its point of inception,Siliguri City,India.Accordingly,a criteria-based evaluation of four railway station districts(New Jalpaiguri,Siliguri Town,Siliguri Junction,and Sukna)in Siliguri and its surroundings was performed.The information regarding the selected four railway station districts is obtained through field observation and key informant consultation,supplemented by published literature and remote sensing data.This evaluation is succeeded by the strengths,weaknesses,opportunities and threats(SWOT)analysis accentuating the potential strengths,weaknesses,opportunities and threats associated with the selected four railway station districts and their prospects to become the potential Railwayscape.The results of this research show that there is no railway station district in Siliguri that can fully meet the demands of the locals and tourists,therefore,relfecting a lack of awareness of the historical values of these districts.The results also indicate that there are significant differences in the relative potentials of railway station districts to become the Railwayscape in urban environment.The outcomes of this research,therefore,are expected to encourage policy-making insitutions and practitioners to realise the‘place value’of some railway station districts and their potentials to yield better economic,social and structural virtue for a wide range of actors.展开更多
Grain production space reconstruction referred to the changes in the quantity,quality and pattern of grain produc-tion space caused by functional tradeoffs and conflicts between grain production space,urban-rural deve...Grain production space reconstruction referred to the changes in the quantity,quality and pattern of grain produc-tion space caused by functional tradeoffs and conflicts between grain production space,urban-rural development space,and ecological service space.Exploring tradeoffs between land system functions caused by grain produc-tion space reconstruction was particularly important for ensuring food security,promoting the construction of ecological civilization,and achieving sustainable development.Therefore,this study identified four relationships of land system functions during the process of grain production space reconstruction(1980-2018)in China by using Set Pair Analysis.Research results showed that the reconstruction of grain production space was achieved mainly through three pathways:Grain for Green,deforestation and reclamation,and urban expansion.Generally,ecological service had spatial negative correlation with grain production,economic development and population carrying capacity(P<0.01),but grain production,economic development and population carrying capacity were positively correlated with each other(P<0.01).In the process of grain production space reconstruction,eco-logical services and economic development,ecological services and population carrying capacity had all shown inverse synergies;there was a tradeoffbetween grain production and ecological services,a codirectional tradeoffbetween grain production and economic development,but a strong synergy between economic development and population carrying capacity.However,the functions of land systems only appeared as synergies or tradeoffs,and there were no inverse synergies and codirectional tradeoffs in the separate processes of Grain for Green,deforestation and reclamation,and urban expansion.It can be concluded that the relationships between land system functions were relatively simple in a single process,but it became complex and diverse when multiple processes were integrated for system analysis.展开更多
The rise of the ancient Silk Road is a model of cross-nation production of space in early human history. During the Western Han Dynasty, after a passage way to the Western regions was "hollowed out" and secu...The rise of the ancient Silk Road is a model of cross-nation production of space in early human history. During the Western Han Dynasty, after a passage way to the Western regions was "hollowed out" and secured, commerce and trade along the route boomed, people started to form clusters, and towns and cities were established. Since the late Tang Dynasty, under the combined effects of natural disasters and manmade misfortunes, regions along the Silk Road in Northwest China were severely depopulated, the towns and cities declined, the ecological environment became fragile, and the social space in West China shrank dramatically. The West Development Strategy later launched by the People' s Republic of China had its focus on optimization and reconstruction of domestic social space, whereas the Belt and Road Initiative(referring respectively to "the Silk Road Economic Belt", hereinafter "the Belt", and "the 21 st-Century Maritime Silk Road", " the Road") is rooted in the planning of space for long-term development and production. In building the Belt and Road, we should take the initiative and necessary steps to manage sound top-level designs; further break down the space alienation emanating from the domestic administrative divisions, and stick to the policy of all around opening up; base the endeavor on the new types of urbanization and strengthen social construction to optimize spatial structures; pay attention to the leading role of space consumption by vigorously developing Silk Road tourism; enhance the transportation and communication infrastructure in the node cities to achieve seamless docking and deep-level integration of both social space and natural space along the Belt and Road.展开更多
Traditional village production space is the basis of villagers’ survival and village development.Nowadays,its production function has been lost,but it still has ecological and cultural value.The formation of traditio...Traditional village production space is the basis of villagers’ survival and village development.Nowadays,its production function has been lost,but it still has ecological and cultural value.The formation of traditional village production space in the Pearl River Delta is closely related to the water system,soil,geology and landform,and three types of production space,including water transportation,agricultural production and manual workshop,have been formed.It has strong ecological adaptability,forms pastoral scenery with unique water village characteristics,and is closely related to the development of the village and the livelihood of the villagers.Under the influence of urbanization,they have undergone great changes,which are manifested in erosion and fragmentation.Therefore,they should be protected,inherited and developed.展开更多
Farm is a vital image in Doris Lessing’s fiction,which is also a result of colonial space production.Through a series of discriminative land policies in a colonial society,the white farmers implement labour exploitat...Farm is a vital image in Doris Lessing’s fiction,which is also a result of colonial space production.Through a series of discriminative land policies in a colonial society,the white farmers implement labour exploitation towards natives.Meanwhile,this space also presents various contradictions among whites.Moreover,colonial space production also leads to the deconstruction of natural space.Lessing’s farm writing reveals her nostalgia of the natural landscape when the farm hasn’t been involved with the capitalist space production and her concern for human beings’unity.展开更多
It is shown that in Euclidean space with any number of spatial dimensions more than three, the Lorentz transform holds true if the proper time of each elementary particle is proportional to the length of its path in t...It is shown that in Euclidean space with any number of spatial dimensions more than three, the Lorentz transform holds true if the proper time of each elementary particle is proportional to the length of its path in the extra-dimensional subspace, and all elementary particles move at the speed of light in the complete space. The six-dimensional treatment of the Coulomb force of interaction between two charges is given. The electric force is due to the motion of charges in the extra-dimensional subspace and is equal to the corresponding Lorentz force.展开更多
By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established...By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.展开更多
We study Hausdorff operators on the product Besov space B0,1 1 (Rn ×Rm) and on the local product Hardy space h1 (Rn ×Rm). We establish some boundedness criteria for Hausdorff operators on these function ...We study Hausdorff operators on the product Besov space B0,1 1 (Rn ×Rm) and on the local product Hardy space h1 (Rn ×Rm). We establish some boundedness criteria for Hausdorff operators on these function spaces.展开更多
In this article, we obtain the sharp bounds from LP(Gn) to the space wLP(Gn) for Hardy operators on product spaces. More generally, the precise norms of Hardy operators on product spaces from LP(Gn) to the space...In this article, we obtain the sharp bounds from LP(Gn) to the space wLP(Gn) for Hardy operators on product spaces. More generally, the precise norms of Hardy operators on product spaces from LP(Gn) to the space LPI (Gn) are obtained.展开更多
By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established...By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.展开更多
By means of vector-valued product Calderón-Zygmund operators and some subtle estimates,the boundedness in product Hardy spaces on R^n × R^m of Calderón-Zygmund operators introduced by J.L. Journé i...By means of vector-valued product Calderón-Zygmund operators and some subtle estimates,the boundedness in product Hardy spaces on R^n × R^m of Calderón-Zygmund operators introduced by J.L. Journé is established.展开更多
In this survey report, we shall mainly summarize some recent progress, interesting problems and typical methods used in the theory related to rough Marcinkiewicz integrals and rough singular integrals on product space...In this survey report, we shall mainly summarize some recent progress, interesting problems and typical methods used in the theory related to rough Marcinkiewicz integrals and rough singular integrals on product spaces. In addition, we give new proofs for some known results.展开更多
Let {(Xi, Si, μi) : i ℃ N} be a sequence of probability measure spaces and (*Xi, L(*Si), L(*μi)) be the Loeb measure space with respect to (Xi, Si, μi) for i ℃ N. Let X =× Xi, S = ×Si,μ = ×μi. We...Let {(Xi, Si, μi) : i ℃ N} be a sequence of probability measure spaces and (*Xi, L(*Si), L(*μi)) be the Loeb measure space with respect to (Xi, Si, μi) for i ℃ N. Let X =× Xi, S = ×Si,μ = ×μi. We prove that × L(*Si) CL(*S) and in embedding meaning.展开更多
基金supported by the Institute of Atmospheric Environment,China Meteorological Administration,Shenyang(Grant No.2021SYIAEKFMS27)Key Laboratory of Farm Building in Structure and Construction,Ministry of Agriculture and Rural Affairs,P.R.China(Grant No.202003)the National Foundation of China Scholarship Council(Grant No.202206040102).
文摘The agricultural production space,as where and how much each agricultural product grows,plays a vital role in meeting the increasing and diverse food demands.Previous studies on agricultural production patterns have predominantly centered on individual or specific crop types,using methods such as remote sensing or statistical metrological analysis.In this study,we characterize the agricultural production space(APS)by bipartite network connecting agricultural products and provinces,to reveal the relatedness between diverse agricultural products and the spatiotemporal characteristic of provincial production capabilities in China.The results show that core products are cereal,pork,melon,and pome fruit;meanwhile the milk,grape,and fiber crop show an upward trend in centrality,which is in line with diet structure changes in China over the past decades.The little changes in community components and structures of agricultural products and provinces reveal that agricultural production patterns in China are relatively stable.Additionally,identified provincial communities closely resemble China's agricultural natural zones.Furthermore,the observed growth in production capabilities in North and Northeast China implies their potential focus areas for future agricultural production.Despite the superior production capa-bilities of southern provinces,recent years have witnessed a notable decline,warranting special attentions.The findings provide a comprehensive perspective for understanding the complex relationship of agricultural prod-ucts'relatedness,production capabilities and production patterns,which serve as a reference for the agricultural spatial optimization and agricultural sustainable development.
文摘For analytic functions u,ψin the unit disk D in the complex plane and an analytic self-mapφof D,we describe in this paper the boundedness and compactness of product type operators T_(u,ψ,φ)f(z)=u(z)f(φ(z))+ψ(z)f'(φ(z)),z∈D,acting between weighted Bergman spaces induced by a doubling weight and a Bloch type space with a radial weight.
文摘Taking Zhaoyu Historical City in Qixian County as an example,this paper explores the production process of tourism space in Zhaoyu Historical City in the context of consumption,based on Lefebvre's triadic dialectic theory.The study reveals that,driven by the development of tourism,subjects such as the government and planners possess absolute dominance over spatial representations,while residents demonstrate receptive and adaptive action strategies and social relations are reproduced,presenting a harmonious state.Further exploring the tourism community in the environmental performance of the subject of action,social relations,consumption demand,daily life practice,cultural capital,etc.,the daily life practice of the tourism community has transcended the original logic of tourism spatial production and has a certain extension.The mechanism analysis in this paper can help guide the healthy development of tourism space in the neighboring historical cities or communities and achieve the dual purpose of promoting the economic development of the community and heritage protection.
基金Under the auspices of the National Basic Research Program of China(No.2015CB452705)
文摘The contradiction between the shortage of land for agriculture due to rapid expansion of industrialization and urbanization and increasing population pressure is projected to impose great threats to future food security.Agricultural land suitability evaluation is an effective approach to improve the utilization of land resources for crop production and thus enhance the capacity of food provision.In this study, we evaluated the land suitability for agriculture of the production space in the Taihang Mountains by three steps: establishing indicator system, determining weights for indicators, and constructing a fuzzy matter-element model to assess the grades of suitability.Results showed that the land suitability had a significant linear correlation with potential crop yields, indicating our evaluation was effective to predict crop production.The spatial pattern of land suitability for crop production demonstrated that land with higher suitability was generally located in piedmont plains and basins, while land with lower suitability was mostly situated in mountainous areas.The area of highly, moderately, marginally suitable and unsuitable land for agriculture was 32.13%, 28.58%, 37.49% and 1.80% of the production space, respectively.However, the correlation degree analysis indicated that the requirements of these four suitability grades were currently not satisfied but could be potentially fulfilled.In terms of indicator weights, soil properties were much more important than topography and location conditions to influence the grades of suitability.Among all indicators, slope, soil organic matter, soil texture and soil depth were the most influential factors, so slope farming prevention and organic fertilization were most likely to improve land suitability for agriculture.Compared the outputs of our land suitability evaluation model with the distribution of the existing croplands, we found that about 66.52% of marginally suitable and 54.55% of unsuitable land for agriculture were currently used for croplands.Therefore, de-farming policy should be implemented in areas of these two suitability grades.In contrast, cropland expansion was encouraged in the land that was highly or moderately suitable for agriculture.Our evaluation of agricultural land suitability is beneficial for future land use planning and decision-making in the Taihang Mountains.
基金University Grants Commission for the Junior Research Fellowship(Ref No.190510006296).
文摘For a long time,it has been argued that the theories and practices devoted to urban planning and management should conform to the fundamental role of planning policies in the production of urban space,but not merely the spatial distribution of the produced services.Towards this wider connotation,this study introduces the notion of Railwayscape,grounded on the theory of‘The Production of Space’,to examine the role of railway station districts as catalysts of urban development through the social production of urban space.The present research sets out to establish the notion of Railwayscape and apply it in a railway heritage,i.e.,the Darjeeling Himalayan Railway(DHR)and its point of inception,Siliguri City,India.Accordingly,a criteria-based evaluation of four railway station districts(New Jalpaiguri,Siliguri Town,Siliguri Junction,and Sukna)in Siliguri and its surroundings was performed.The information regarding the selected four railway station districts is obtained through field observation and key informant consultation,supplemented by published literature and remote sensing data.This evaluation is succeeded by the strengths,weaknesses,opportunities and threats(SWOT)analysis accentuating the potential strengths,weaknesses,opportunities and threats associated with the selected four railway station districts and their prospects to become the potential Railwayscape.The results of this research show that there is no railway station district in Siliguri that can fully meet the demands of the locals and tourists,therefore,relfecting a lack of awareness of the historical values of these districts.The results also indicate that there are significant differences in the relative potentials of railway station districts to become the Railwayscape in urban environment.The outcomes of this research,therefore,are expected to encourage policy-making insitutions and practitioners to realise the‘place value’of some railway station districts and their potentials to yield better economic,social and structural virtue for a wide range of actors.
基金conducted under the auspice of National Natural Science Foundation of China(Grant No.41701094).
文摘Grain production space reconstruction referred to the changes in the quantity,quality and pattern of grain produc-tion space caused by functional tradeoffs and conflicts between grain production space,urban-rural development space,and ecological service space.Exploring tradeoffs between land system functions caused by grain produc-tion space reconstruction was particularly important for ensuring food security,promoting the construction of ecological civilization,and achieving sustainable development.Therefore,this study identified four relationships of land system functions during the process of grain production space reconstruction(1980-2018)in China by using Set Pair Analysis.Research results showed that the reconstruction of grain production space was achieved mainly through three pathways:Grain for Green,deforestation and reclamation,and urban expansion.Generally,ecological service had spatial negative correlation with grain production,economic development and population carrying capacity(P<0.01),but grain production,economic development and population carrying capacity were positively correlated with each other(P<0.01).In the process of grain production space reconstruction,eco-logical services and economic development,ecological services and population carrying capacity had all shown inverse synergies;there was a tradeoffbetween grain production and ecological services,a codirectional tradeoffbetween grain production and economic development,but a strong synergy between economic development and population carrying capacity.However,the functions of land systems only appeared as synergies or tradeoffs,and there were no inverse synergies and codirectional tradeoffs in the separate processes of Grain for Green,deforestation and reclamation,and urban expansion.It can be concluded that the relationships between land system functions were relatively simple in a single process,but it became complex and diverse when multiple processes were integrated for system analysis.
基金one of the phased objectives of the Shaanxi Academy of Social Sciences' 2014 key research project "Social Construction of the Western China Society from the Production of Space Perspective"(Project No.:14ZD02)
文摘The rise of the ancient Silk Road is a model of cross-nation production of space in early human history. During the Western Han Dynasty, after a passage way to the Western regions was "hollowed out" and secured, commerce and trade along the route boomed, people started to form clusters, and towns and cities were established. Since the late Tang Dynasty, under the combined effects of natural disasters and manmade misfortunes, regions along the Silk Road in Northwest China were severely depopulated, the towns and cities declined, the ecological environment became fragile, and the social space in West China shrank dramatically. The West Development Strategy later launched by the People' s Republic of China had its focus on optimization and reconstruction of domestic social space, whereas the Belt and Road Initiative(referring respectively to "the Silk Road Economic Belt", hereinafter "the Belt", and "the 21 st-Century Maritime Silk Road", " the Road") is rooted in the planning of space for long-term development and production. In building the Belt and Road, we should take the initiative and necessary steps to manage sound top-level designs; further break down the space alienation emanating from the domestic administrative divisions, and stick to the policy of all around opening up; base the endeavor on the new types of urbanization and strengthen social construction to optimize spatial structures; pay attention to the leading role of space consumption by vigorously developing Silk Road tourism; enhance the transportation and communication infrastructure in the node cities to achieve seamless docking and deep-level integration of both social space and natural space along the Belt and Road.
基金Sponsored by The 2017 Discipline Co-construction Project of the 13^(th) Five-Year Plan of Philosophy and Social Sciences in Guangdong Province (GD17XGL62)。
文摘Traditional village production space is the basis of villagers’ survival and village development.Nowadays,its production function has been lost,but it still has ecological and cultural value.The formation of traditional village production space in the Pearl River Delta is closely related to the water system,soil,geology and landform,and three types of production space,including water transportation,agricultural production and manual workshop,have been formed.It has strong ecological adaptability,forms pastoral scenery with unique water village characteristics,and is closely related to the development of the village and the livelihood of the villagers.Under the influence of urbanization,they have undergone great changes,which are manifested in erosion and fragmentation.Therefore,they should be protected,inherited and developed.
文摘Farm is a vital image in Doris Lessing’s fiction,which is also a result of colonial space production.Through a series of discriminative land policies in a colonial society,the white farmers implement labour exploitation towards natives.Meanwhile,this space also presents various contradictions among whites.Moreover,colonial space production also leads to the deconstruction of natural space.Lessing’s farm writing reveals her nostalgia of the natural landscape when the farm hasn’t been involved with the capitalist space production and her concern for human beings’unity.
文摘It is shown that in Euclidean space with any number of spatial dimensions more than three, the Lorentz transform holds true if the proper time of each elementary particle is proportional to the length of its path in the extra-dimensional subspace, and all elementary particles move at the speed of light in the complete space. The six-dimensional treatment of the Coulomb force of interaction between two charges is given. The electric force is due to the motion of charges in the extra-dimensional subspace and is equal to the corresponding Lorentz force.
文摘By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.
基金Supported by the National Natural Science Foundation of China(10931001, 10871173 and 11026104)
文摘We study Hausdorff operators on the product Besov space B0,1 1 (Rn ×Rm) and on the local product Hardy space h1 (Rn ×Rm). We establish some boundedness criteria for Hausdorff operators on these function spaces.
基金supported by NSFC(11471309,11271162,and11561062)Project of Henan Provincial Department of Education(18A110028)+1 种基金the Nanhu Scholar Program for Young Scholars of XYNUDoctoral Scientific Research Startup Fund of Xinyang Normal University(2016)
文摘In this article, we obtain the sharp bounds from LP(Gn) to the space wLP(Gn) for Hardy operators on product spaces. More generally, the precise norms of Hardy operators on product spaces from LP(Gn) to the space LPI (Gn) are obtained.
文摘By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.
基金supported by the National Natural Science Foundation of China(10871025)
文摘By means of vector-valued product Calderón-Zygmund operators and some subtle estimates,the boundedness in product Hardy spaces on R^n × R^m of Calderón-Zygmund operators introduced by J.L. Journé is established.
基金the Project of Development Plan of the State Key Fundamental Research Major Project of NNSFC,and NSFZJ.
文摘In this survey report, we shall mainly summarize some recent progress, interesting problems and typical methods used in the theory related to rough Marcinkiewicz integrals and rough singular integrals on product spaces. In addition, we give new proofs for some known results.
基金The Special Science Foundation (00jk207) of the Educational Committee of Shaanxi Province.
文摘Let {(Xi, Si, μi) : i ℃ N} be a sequence of probability measure spaces and (*Xi, L(*Si), L(*μi)) be the Loeb measure space with respect to (Xi, Si, μi) for i ℃ N. Let X =× Xi, S = ×Si,μ = ×μi. We prove that × L(*Si) CL(*S) and in embedding meaning.