This paper is a continuation of recent work by Guo-Xiang-Zheng[10].We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivière equation △^{2}u=△(V▽u)+div(w▽...This paper is a continuation of recent work by Guo-Xiang-Zheng[10].We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivière equation △^{2}u=△(V▽u)+div(w▽u)+(▽ω+F)·▽u+f in B^(4),under the smallest regularity assumptions of V,ω,ω,F,where f belongs to some Morrey spaces.This work was motivated by many geometrical problems such as the flow of biharmonic mappings.Our results deepens the Lp type regularity theory of[10],and generalizes the work of Du,Kang and Wang[4]on a second order problem to our fourth order problems.展开更多
In this paper,we investigate sufficient and necessary conditions such that generalized Forelli-Rudin type operators T_(λ,τ,k),S_(λ,τ,k),Q_(λ,τ,k)and R_(λ,τ,k)are bounded between Lebesgue type spaces.In order t...In this paper,we investigate sufficient and necessary conditions such that generalized Forelli-Rudin type operators T_(λ,τ,k),S_(λ,τ,k),Q_(λ,τ,k)and R_(λ,τ,k)are bounded between Lebesgue type spaces.In order to prove the main results,we first give some bidirectional estimates for several typical integrals.展开更多
In this article,we investigate the(big) Hankel operator H_(f) on the Hardy spaces of bounded strongly pseudoconvex domains Ω in C^(n).We observe that H_(f ) is bounded on H~p(Ω)(1 <p <∞) if f belongs to BMO a...In this article,we investigate the(big) Hankel operator H_(f) on the Hardy spaces of bounded strongly pseudoconvex domains Ω in C^(n).We observe that H_(f ) is bounded on H~p(Ω)(1 <p <∞) if f belongs to BMO and we obtain some characterizations for Hf on H^(2)(Ω) of other pseudoconvex domains.In these arguments,Amar's L^(p)-estimations and Berndtsson's L^(2)-estimations for solutions of the ■_(b)-equation play a crucial role.In addition,we solve Gleason's problem for Hardy spaces H^(p)(Ω)(1 ≤p≤∞) of bounded strongly pseudoconvex domains.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
Urbanization has profound impacts on ecological environments. Green spaces are a vital component of urban ecosystems and play a crucial role in maintaining ecological balance and enhancing sustainability. This study a...Urbanization has profound impacts on ecological environments. Green spaces are a vital component of urban ecosystems and play a crucial role in maintaining ecological balance and enhancing sustainability. This study aimed to investigate the community composition characteristics of butterflies in urban green spaces within the context of rapid urbanization. Simultaneously, it explored the status and differences in butterfly taxonomic diversity, functional diversity, and functional traits among different types of urban green spaces, regions, and urban gradients to provide relevant insights for further improving urban green space quality and promoting biodiversity conservation. We conducted a year-long survey of 80 green spaces across different urban regions and ring roads within Hefei City, Anhui Province, with monthly sampling intervals over 187 transects. A total of 4822 butterflies, belonging to 5 families, 17 subfamilies, 40 genera, and 55 species were identified. The species richness, Shannon, Simpson, functional richness, and Rao's quadratic entropy indices of butterflies in urban park green spaces were all significantly higher than those in residential and street green spaces(P < 0.05). Differences in butterfly diversity and functional traits among different urban regions and ring roads were relatively minor, and small-sized, multivoltine, and long flying duration butterflies dominated urban green spaces. Overall, these spaces offer more favorable habitats for butterflies. However, some residential green spaces and street green spaces demonstrate potential for butterfly conservation.展开更多
Assume that L is a non-negative self-adjoint operator on L^(2)(ℝ^(n))with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝ^(n) satisfying som...Assume that L is a non-negative self-adjoint operator on L^(2)(ℝ^(n))with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝ^(n) satisfying some mild assumptions.Let HX,L(ℝ^(n))be the Hardy space associated with both X and L,which is defined by the Lusin area function related to the semigroup generated by L.In this article,the authors establish various maximal function characterizations of the Hardy space HX,L(ℝ^(n))and then apply these characterizations to obtain the solvability of the related Cauchy problem.These results have a wide range of generality and,in particular,the specific spaces X to which these results can be applied include the weighted space,the variable space,the mixed-norm space,the Orlicz space,the Orlicz-slice space,and the Morrey space.Moreover,the obtained maximal function characterizations of the mixed-norm Hardy space,the Orlicz-slice Hardy space,and the Morrey-Hardy space associated with L are completely new.展开更多
Letμbe a positive Borel measure on the interval[0,1).The Hankel matrix■with entriesμn,k=μn+k,whereμn=⨜[0,1)tndμ(t),induces,formally,the operator■where■is an analytic function in.We characterize the measuresμf...Letμbe a positive Borel measure on the interval[0,1).The Hankel matrix■with entriesμn,k=μn+k,whereμn=⨜[0,1)tndμ(t),induces,formally,the operator■where■is an analytic function in.We characterize the measuresμfor which■is bounded(resp.,compact)operator from the logarithmic Bloch space■into the Bergman space■,where 0≤α<∞,0<p<∞.We also characterize the measuresμfor which■is bounded(resp.,compact)operator from the logarithmic Bloch space■into the classical Bloch space■.展开更多
We consider dual Toeplitz operators on the orthogonal complements of the FockSobolev spaces of all nonnegative real orders.First,for symbols in a certain class containing all bounded functions,we study the problem of ...We consider dual Toeplitz operators on the orthogonal complements of the FockSobolev spaces of all nonnegative real orders.First,for symbols in a certain class containing all bounded functions,we study the problem of when an operator which is finite sums of the dual Toeplitz products is compact or zero.Next,for bounded symbols,we construct a symbol map and exhibit a short exact sequence associated with the C^(*)-algebra generated by all dual Toeplitz operators with bounded symbols.展开更多
In this paper,we introduce the weighted multilinear p-adic Hardy operator and weighted multilinear p-adic Ces`aro operator,we also obtain the boundedness of these two operators on the product of p-adic Herz spaces and...In this paper,we introduce the weighted multilinear p-adic Hardy operator and weighted multilinear p-adic Ces`aro operator,we also obtain the boundedness of these two operators on the product of p-adic Herz spaces and p-adic Morrey-Herz spaces,the corresponding operator norms are also established in each case.Moreover,the boundedness of commutators of these two operators with symbols in central bounded mean oscillation spaces and Lipschitz spaces on p-adic Morrey-Herz spaces are also given.展开更多
Urbanization often changes bird species richness and affects the functional diversity.Therefore,understanding these changes helps city planners improve green space design and land use planning.Our study used multiple ...Urbanization often changes bird species richness and affects the functional diversity.Therefore,understanding these changes helps city planners improve green space design and land use planning.Our study used multiple datasets to explore the effects of land-scape patterns and natural environments on the functional diversity of birds in urban parks and campuses in the eastern and northwest-ern regions of China.Firstly,we used the data to calculate birds of the functional richness(FRic),functional evenness(FEve),and func-tional divergence(FDiv)of 68 urban spaces in the eastern and northwestern regions of China.Further,we established generalized linear models of natural factors,human factors,and functional diversity.Results showed more bird species with unique traits were in the north-western region.This may be because the earlier urbanization in the eastern region filtered out urban-sensitive species,leaving behind urban adapters.Moreover,we found that the fractal dimension index was the most significant positive factor of FRic in the eastern re-gion but the most significant negative factor of FDiv.Elevation was the most significant negative influence factor of FEve in the eastern region,but it was the most potent positive influence factor of FRic in the northwestern region.Population density had a significant posit-ive effect on FDiv in the northwestern region.However,green space areas significantly negatively impacted FEve in the northwestern region.In addition,birds in parks in both regions had more functional traits than those on campuses,possibly because of the larger green space in parks,which may contain more fragments of native vegetation and reduce human interference.Our study suggests that pre-serving more original vegetation and reducing human disturbance in cities can increase the functional diversity of urban birds and im-prove urban ecosystem functions.展开更多
In this paper,by characterizing Carleson measures,we investigate a class of bounded Toeplitz operator between weighted Bergman spaces with Békolléweights over the half-plane for all index choices.
基金supported by the National Natural Science Foundation of China(12271296,12271195).
文摘This paper is a continuation of recent work by Guo-Xiang-Zheng[10].We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivière equation △^{2}u=△(V▽u)+div(w▽u)+(▽ω+F)·▽u+f in B^(4),under the smallest regularity assumptions of V,ω,ω,F,where f belongs to some Morrey spaces.This work was motivated by many geometrical problems such as the flow of biharmonic mappings.Our results deepens the Lp type regularity theory of[10],and generalizes the work of Du,Kang and Wang[4]on a second order problem to our fourth order problems.
基金supported by the Natural Science Foundation of Hunan Province of China(2022JJ30369)the Education Department Important Foundation of Hunan Province in China(23A0095)。
文摘In this paper,we investigate sufficient and necessary conditions such that generalized Forelli-Rudin type operators T_(λ,τ,k),S_(λ,τ,k),Q_(λ,τ,k)and R_(λ,τ,k)are bounded between Lebesgue type spaces.In order to prove the main results,we first give some bidirectional estimates for several typical integrals.
基金supported by the National Natural Science Foundation of China(12271101)。
文摘In this article,we investigate the(big) Hankel operator H_(f) on the Hardy spaces of bounded strongly pseudoconvex domains Ω in C^(n).We observe that H_(f ) is bounded on H~p(Ω)(1 <p <∞) if f belongs to BMO and we obtain some characterizations for Hf on H^(2)(Ω) of other pseudoconvex domains.In these arguments,Amar's L^(p)-estimations and Berndtsson's L^(2)-estimations for solutions of the ■_(b)-equation play a crucial role.In addition,we solve Gleason's problem for Hardy spaces H^(p)(Ω)(1 ≤p≤∞) of bounded strongly pseudoconvex domains.
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.
基金funded by the National Non Profit Research Institutions of the Chinese Academy of Forestry(CAFYBB2020ZB008)National Natural Science Foundation of China(32371936)the Research Projects in Anhui Universities in 2022(natural sciences)(2022AH051874).
文摘Urbanization has profound impacts on ecological environments. Green spaces are a vital component of urban ecosystems and play a crucial role in maintaining ecological balance and enhancing sustainability. This study aimed to investigate the community composition characteristics of butterflies in urban green spaces within the context of rapid urbanization. Simultaneously, it explored the status and differences in butterfly taxonomic diversity, functional diversity, and functional traits among different types of urban green spaces, regions, and urban gradients to provide relevant insights for further improving urban green space quality and promoting biodiversity conservation. We conducted a year-long survey of 80 green spaces across different urban regions and ring roads within Hefei City, Anhui Province, with monthly sampling intervals over 187 transects. A total of 4822 butterflies, belonging to 5 families, 17 subfamilies, 40 genera, and 55 species were identified. The species richness, Shannon, Simpson, functional richness, and Rao's quadratic entropy indices of butterflies in urban park green spaces were all significantly higher than those in residential and street green spaces(P < 0.05). Differences in butterfly diversity and functional traits among different urban regions and ring roads were relatively minor, and small-sized, multivoltine, and long flying duration butterflies dominated urban green spaces. Overall, these spaces offer more favorable habitats for butterflies. However, some residential green spaces and street green spaces demonstrate potential for butterfly conservation.
基金supported by the National Key Research and Development Program of China(2020YFA0712900)the National Natural Science Foundation of China(12371093,12071197,12122102 and 12071431)+2 种基金the Key Project of Gansu Provincial National Science Foundation(23JRRA1022)the Fundamental Research Funds for the Central Universities(2233300008 and lzujbky-2021-ey18)the Innovative Groups of Basic Research in Gansu Province(22JR5RA391).
文摘Assume that L is a non-negative self-adjoint operator on L^(2)(ℝ^(n))with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝ^(n) satisfying some mild assumptions.Let HX,L(ℝ^(n))be the Hardy space associated with both X and L,which is defined by the Lusin area function related to the semigroup generated by L.In this article,the authors establish various maximal function characterizations of the Hardy space HX,L(ℝ^(n))and then apply these characterizations to obtain the solvability of the related Cauchy problem.These results have a wide range of generality and,in particular,the specific spaces X to which these results can be applied include the weighted space,the variable space,the mixed-norm space,the Orlicz space,the Orlicz-slice space,and the Morrey space.Moreover,the obtained maximal function characterizations of the mixed-norm Hardy space,the Orlicz-slice Hardy space,and the Morrey-Hardy space associated with L are completely new.
基金supported by Zhejiang Provincial Natural Science Foundation of China(LY23A010003).
文摘Letμbe a positive Borel measure on the interval[0,1).The Hankel matrix■with entriesμn,k=μn+k,whereμn=⨜[0,1)tndμ(t),induces,formally,the operator■where■is an analytic function in.We characterize the measuresμfor which■is bounded(resp.,compact)operator from the logarithmic Bloch space■into the Bergman space■,where 0≤α<∞,0<p<∞.We also characterize the measuresμfor which■is bounded(resp.,compact)operator from the logarithmic Bloch space■into the classical Bloch space■.
基金supported by the NSFC(12271134,11771401)supported by the Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education(NRF-2019R1I1A3A01041943)。
文摘We consider dual Toeplitz operators on the orthogonal complements of the FockSobolev spaces of all nonnegative real orders.First,for symbols in a certain class containing all bounded functions,we study the problem of when an operator which is finite sums of the dual Toeplitz products is compact or zero.Next,for bounded symbols,we construct a symbol map and exhibit a short exact sequence associated with the C^(*)-algebra generated by all dual Toeplitz operators with bounded symbols.
文摘In this paper,we introduce the weighted multilinear p-adic Hardy operator and weighted multilinear p-adic Ces`aro operator,we also obtain the boundedness of these two operators on the product of p-adic Herz spaces and p-adic Morrey-Herz spaces,the corresponding operator norms are also established in each case.Moreover,the boundedness of commutators of these two operators with symbols in central bounded mean oscillation spaces and Lipschitz spaces on p-adic Morrey-Herz spaces are also given.
基金Under the auspices of the Innovation Program of Chinese Academy of Agricultural Sciences(No.CAAS-STNY-2024)。
文摘Urbanization often changes bird species richness and affects the functional diversity.Therefore,understanding these changes helps city planners improve green space design and land use planning.Our study used multiple datasets to explore the effects of land-scape patterns and natural environments on the functional diversity of birds in urban parks and campuses in the eastern and northwest-ern regions of China.Firstly,we used the data to calculate birds of the functional richness(FRic),functional evenness(FEve),and func-tional divergence(FDiv)of 68 urban spaces in the eastern and northwestern regions of China.Further,we established generalized linear models of natural factors,human factors,and functional diversity.Results showed more bird species with unique traits were in the north-western region.This may be because the earlier urbanization in the eastern region filtered out urban-sensitive species,leaving behind urban adapters.Moreover,we found that the fractal dimension index was the most significant positive factor of FRic in the eastern re-gion but the most significant negative factor of FDiv.Elevation was the most significant negative influence factor of FEve in the eastern region,but it was the most potent positive influence factor of FRic in the northwestern region.Population density had a significant posit-ive effect on FDiv in the northwestern region.However,green space areas significantly negatively impacted FEve in the northwestern region.In addition,birds in parks in both regions had more functional traits than those on campuses,possibly because of the larger green space in parks,which may contain more fragments of native vegetation and reduce human interference.Our study suggests that pre-serving more original vegetation and reducing human disturbance in cities can increase the functional diversity of urban birds and im-prove urban ecosystem functions.
基金supported by the Natural Science Foundation of China(12271134)the Shanxi Scholarship Council of China(2020–089)the Fund Program for the Scientific Activities of Selected Returned Overseas Professionals in Shanxi Province(20200019).
文摘In this paper,by characterizing Carleson measures,we investigate a class of bounded Toeplitz operator between weighted Bergman spaces with Békolléweights over the half-plane for all index choices.
