Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting...Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality estimates.In this paper,we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition.展开更多
A locally convex space is said to be a Gateaux differentiability space (GDS) provided every continuous convex function defined on a nonempty convex open subset D of the space is densely Gateaux differentiable in .D.Th...A locally convex space is said to be a Gateaux differentiability space (GDS) provided every continuous convex function defined on a nonempty convex open subset D of the space is densely Gateaux differentiable in .D.This paper shows that the product of a GDS and a family of separable Prechet spaces is a GDS,and that the product of a GDS and an arbitrary locally convex space endowed with the weak topology is a GDS.展开更多
In this paper, we use the well known KKM type theorem for generalized convex spaces due to Park (Elements of the KKM theory for generalized convex spaces, Korean J. Comp. Appl. Math., 7(2000), 1-28) to obtain an a...In this paper, we use the well known KKM type theorem for generalized convex spaces due to Park (Elements of the KKM theory for generalized convex spaces, Korean J. Comp. Appl. Math., 7(2000), 1-28) to obtain an almost fixed point theorem for upper [resp., lower] semicontinuous multimaps in locally G-convex spaces, and then give a fixed point theorem for upper semicontinuous multimap with closed Γ-convex values.展开更多
This paper gives internal characterizations of some sequence covering compact images and compact covering compact images of paracompact locally compact spaces, which improve some results on compact images of locally...This paper gives internal characterizations of some sequence covering compact images and compact covering compact images of paracompact locally compact spaces, which improve some results on compact images of locally compact metric spaces.展开更多
A new class of generalized constrained multiobjective games is introduced and studied in locally FC-uniform spaces without convexity structure where the number of players may be finite or infinite and all payoff funct...A new class of generalized constrained multiobjective games is introduced and studied in locally FC-uniform spaces without convexity structure where the number of players may be finite or infinite and all payoff functions get their values in an infinite-dimensional space. By using a Himmelberg type fixed point theorem in locally FC-uniform spaces due to author, some existence theorems of weak Paxeto equilibria for the generalized constrained multiobjective games are established in locally FC-uniform spaces. These theorems improve, unify and generalize the corresponding results in recent literatures.展开更多
In this paper, we investigate local properties in the system of completely 1-summing mapping spaces. We introduce notions of injectivity, local reflexivity, exactness, nuclearity and finite-representability in the sys...In this paper, we investigate local properties in the system of completely 1-summing mapping spaces. We introduce notions of injectivity, local reflexivity, exactness, nuclearity and finite-representability in the system of completely 1-summing mapping spaces. First we obtain that if V has WEP, V is locally reflexive in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)) if and only if it is locally reflexive in the system (Ⅰ(⋅,⋅), t(⋅)). Furthermore we prove that an operator space V ⊆ B(H) is exact in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)) if and only if V is finitely representable in {M<sub>n</sub>}<sub>n∈N</sub> in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)). At last, we show that an operator space V is finitely representable in {M<sub>n</sub>}<sub>n∈N</sub> in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)) if and only if V = C.展开更多
In this note we obtain generalization of well known results of carbone and Conti,Sehgal and Singh and Tanimoto concerning the existence of best approximation and simultaneous best approximation of continuous Junctions...In this note we obtain generalization of well known results of carbone and Conti,Sehgal and Singh and Tanimoto concerning the existence of best approximation and simultaneous best approximation of continuous Junctions from the set up of a normed space to the case of a Hausdorff locally convex space.展开更多
First, the notions of the measure of noncompactness and condensing setvalued mappings are introduced in locally FC-uniform spaces without convexity structure. A new existence theorem of maximal elements of a family of...First, the notions of the measure of noncompactness and condensing setvalued mappings are introduced in locally FC-uniform spaces without convexity structure. A new existence theorem of maximal elements of a family of set-valued mappings involving condensing mappings is proved in locally FC-uniform spaces. As applications, some new equilibrium existence theorems of generalized game involving condensing mappings are established in locally FC-uniform spaces. These results improve and generalize some known results in literature to locally FC-uniform spaces. Some further applications of our results to the systems of generalized vector quasi-equilibrium problems will be given in a follow-up paper.展开更多
Some classes of generalized vector quasi-equilibrium problems ( in short, GVQEP) are introduced and studied in locally G-convex spaces which includes most of generalized vector equilibrium problems; generalized vector...Some classes of generalized vector quasi-equilibrium problems ( in short, GVQEP) are introduced and studied in locally G-convex spaces which includes most of generalized vector equilibrium problems; generalized vector variational inequality problems, quasi-equilibrium problems and quasi-variational inequality problems as special cases. First, an equilibrium existence theorem for one person games is proved in locally G-convex spaces.. As applications, some new existence theorems of solutions for the GVQEP are established in noncompact locally G-convex spaces. These results and argument methods are new and completely different from that in recent literature.展开更多
In this paper, the vector-valued regular functions are extended to the locally convex space. The residues theory of the functions in the locally convex space is achieved. Thereby the Cauchy theory and Cauchy integral ...In this paper, the vector-valued regular functions are extended to the locally convex space. The residues theory of the functions in the locally convex space is achieved. Thereby the Cauchy theory and Cauchy integral formula are extended to the locally convex space.展开更多
In this article, we introduce and study some new classes of multi-leader-follower generalized constrained multiobjective games in locally FC-uniform spaces where the number of leaders and followers may be finite or in...In this article, we introduce and study some new classes of multi-leader-follower generalized constrained multiobjective games in locally FC-uniform spaces where the number of leaders and followers may be finite or infinite and the objective functions of the followers obtain their values in infinite-dimensional spaces. Each leader has a constrained correspondence. By using a collective fixed point theorem in locally FC-uniform spaces due to author, some existence theorems of equilibrium points for the multi-leader-follower generalized constrained multiobjective games are established under nonconvex settings. These results generalize some corresponding results in recent literature.展开更多
In this paper, we introduce some new systems of generalized vector quasi-variational inclusion problems and system of generalized vector ideal (resp., proper, Pareto, weak) quasi-optimization problems in locally FC-...In this paper, we introduce some new systems of generalized vector quasi-variational inclusion problems and system of generalized vector ideal (resp., proper, Pareto, weak) quasi-optimization problems in locally FC-uniform spaces without convexity structure. By using the KKM type theorem and Himmelberg type fixed point theorem proposed by the author, some new existence theorems of solutions for the systems of generalized vector quasi-variational inclusion problems are proved. As to its applications, we obtain some existence results of solutions for systems of generalized vector quasi-optimization problems.展开更多
In this paper, we introduce the concept of locally fully convexity. We study the properties of fully convex and locally fully convex Banach spaces and the relations between them. We also give some applications of the ...In this paper, we introduce the concept of locally fully convexity. We study the properties of fully convex and locally fully convex Banach spaces and the relations between them. We also give some applications of the fully convex and locally fully convex Banach spaces.展开更多
In this note, we consider the multipliers on weighted function spaces over totally disconnected locally compact abelian groups (Vilenkin groups). Firstly we show an (H1 ,L ) multiplier result. We also give an (Hap ,Ha...In this note, we consider the multipliers on weighted function spaces over totally disconnected locally compact abelian groups (Vilenkin groups). Firstly we show an (H1 ,L ) multiplier result. We also give an (Hap ,Hap) multiplier result under a similiar condition of Lu Yang type. In section 2, we obtain a result about the boundedness of multipliers on weighted Besov spaces.展开更多
In this paper, we study the characterization of f-Chebyshev radius and f-Chebyshev centers and the existence of f-Chebyshev centers in locally convex spaces.
By introducing the notions of L-spaces and L_r-spaces, a complete generalization of Kalton's closed graph theorem is obtained. It points out the class of L_r-spaces is the maximal class of range spaces for the clo...By introducing the notions of L-spaces and L_r-spaces, a complete generalization of Kalton's closed graph theorem is obtained. It points out the class of L_r-spaces is the maximal class of range spaces for the closed graph theorem when the class of domain spaces is the class of Mackey spaces with weakly * sequentially complete dual.Some examples are constructed showing that the class of L_r-spaces is strictly larger than the class of separable B_r-complete spaces.Some properties of L-spaces and L_r-spaces are discussed and the relations between B-complete (resp. B_r-complete) spaces and L-spaces (resp. L_r-spaces) are given.展开更多
Let (E,γ) be a locally convex space and E′ its conjugate space. AE′ be an equicontinuous set on (E,γ). In this paper,we show that for each sequence {f i}A and {x j}E, if {x j} converges to 0 in (E,γ), then ...Let (E,γ) be a locally convex space and E′ its conjugate space. AE′ be an equicontinuous set on (E,γ). In this paper,we show that for each sequence {f i}A and {x j}E, if {x j} converges to 0 in (E,γ), then we can find a f 0∈E′ and extract subsequences {f n i } and {x n j } such that {f n i } converges to f 0 on {x n j } uniformly. If (E,γ) is metrizable,then we can show that the converse is also valid.展开更多
文摘Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality estimates.In this paper,we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition.
基金Supported by the NSF of China (10071063 and 10471114)
文摘A locally convex space is said to be a Gateaux differentiability space (GDS) provided every continuous convex function defined on a nonempty convex open subset D of the space is densely Gateaux differentiable in .D.This paper shows that the product of a GDS and a family of separable Prechet spaces is a GDS,and that the product of a GDS and an arbitrary locally convex space endowed with the weak topology is a GDS.
文摘In this paper, we use the well known KKM type theorem for generalized convex spaces due to Park (Elements of the KKM theory for generalized convex spaces, Korean J. Comp. Appl. Math., 7(2000), 1-28) to obtain an almost fixed point theorem for upper [resp., lower] semicontinuous multimaps in locally G-convex spaces, and then give a fixed point theorem for upper semicontinuous multimap with closed Γ-convex values.
文摘This paper gives internal characterizations of some sequence covering compact images and compact covering compact images of paracompact locally compact spaces, which improve some results on compact images of locally compact metric spaces.
基金the Natural Science Foundation of Education Department of Sichuan Province of China(No.07ZA092)the Foundation of Taiwan Science Council
文摘A new class of generalized constrained multiobjective games is introduced and studied in locally FC-uniform spaces without convexity structure where the number of players may be finite or infinite and all payoff functions get their values in an infinite-dimensional space. By using a Himmelberg type fixed point theorem in locally FC-uniform spaces due to author, some existence theorems of weak Paxeto equilibria for the generalized constrained multiobjective games are established in locally FC-uniform spaces. These theorems improve, unify and generalize the corresponding results in recent literatures.
文摘In this paper, we investigate local properties in the system of completely 1-summing mapping spaces. We introduce notions of injectivity, local reflexivity, exactness, nuclearity and finite-representability in the system of completely 1-summing mapping spaces. First we obtain that if V has WEP, V is locally reflexive in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)) if and only if it is locally reflexive in the system (Ⅰ(⋅,⋅), t(⋅)). Furthermore we prove that an operator space V ⊆ B(H) is exact in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)) if and only if V is finitely representable in {M<sub>n</sub>}<sub>n∈N</sub> in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)). At last, we show that an operator space V is finitely representable in {M<sub>n</sub>}<sub>n∈N</sub> in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)) if and only if V = C.
文摘In this note we obtain generalization of well known results of carbone and Conti,Sehgal and Singh and Tanimoto concerning the existence of best approximation and simultaneous best approximation of continuous Junctions from the set up of a normed space to the case of a Hausdorff locally convex space.
基金the Natural Science Foundation of Sichuan Education Department of China (Nos.2003A081 and SZD0406)
文摘First, the notions of the measure of noncompactness and condensing setvalued mappings are introduced in locally FC-uniform spaces without convexity structure. A new existence theorem of maximal elements of a family of set-valued mappings involving condensing mappings is proved in locally FC-uniform spaces. As applications, some new equilibrium existence theorems of generalized game involving condensing mappings are established in locally FC-uniform spaces. These results improve and generalize some known results in literature to locally FC-uniform spaces. Some further applications of our results to the systems of generalized vector quasi-equilibrium problems will be given in a follow-up paper.
文摘Some classes of generalized vector quasi-equilibrium problems ( in short, GVQEP) are introduced and studied in locally G-convex spaces which includes most of generalized vector equilibrium problems; generalized vector variational inequality problems, quasi-equilibrium problems and quasi-variational inequality problems as special cases. First, an equilibrium existence theorem for one person games is proved in locally G-convex spaces.. As applications, some new existence theorems of solutions for the GVQEP are established in noncompact locally G-convex spaces. These results and argument methods are new and completely different from that in recent literature.
文摘In this paper, the vector-valued regular functions are extended to the locally convex space. The residues theory of the functions in the locally convex space is achieved. Thereby the Cauchy theory and Cauchy integral formula are extended to the locally convex space.
基金supported by the Scientific Research Fun of Sichuan Normal University(11ZDL01)the Sichuan Province Leading Academic Discipline Project(SZD0406)
文摘In this article, we introduce and study some new classes of multi-leader-follower generalized constrained multiobjective games in locally FC-uniform spaces where the number of leaders and followers may be finite or infinite and the objective functions of the followers obtain their values in infinite-dimensional spaces. Each leader has a constrained correspondence. By using a collective fixed point theorem in locally FC-uniform spaces due to author, some existence theorems of equilibrium points for the multi-leader-follower generalized constrained multiobjective games are established under nonconvex settings. These results generalize some corresponding results in recent literature.
基金supported by the Natural Science Foundation of Sichuan Education Department of China(No. 07ZA092)the Sichuan Province Leading Academic Discipline Project (No. SZD0406)
文摘In this paper, we introduce some new systems of generalized vector quasi-variational inclusion problems and system of generalized vector ideal (resp., proper, Pareto, weak) quasi-optimization problems in locally FC-uniform spaces without convexity structure. By using the KKM type theorem and Himmelberg type fixed point theorem proposed by the author, some new existence theorems of solutions for the systems of generalized vector quasi-variational inclusion problems are proved. As to its applications, we obtain some existence results of solutions for systems of generalized vector quasi-optimization problems.
文摘In this paper, we introduce the concept of locally fully convexity. We study the properties of fully convex and locally fully convex Banach spaces and the relations between them. We also give some applications of the fully convex and locally fully convex Banach spaces.
文摘In this note, we consider the multipliers on weighted function spaces over totally disconnected locally compact abelian groups (Vilenkin groups). Firstly we show an (H1 ,L ) multiplier result. We also give an (Hap ,Hap) multiplier result under a similiar condition of Lu Yang type. In section 2, we obtain a result about the boundedness of multipliers on weighted Besov spaces.
基金Research supported by the National Science Foundation of P.R.China
文摘In this paper, we study the characterization of f-Chebyshev radius and f-Chebyshev centers and the existence of f-Chebyshev centers in locally convex spaces.
文摘By introducing the notions of L-spaces and L_r-spaces, a complete generalization of Kalton's closed graph theorem is obtained. It points out the class of L_r-spaces is the maximal class of range spaces for the closed graph theorem when the class of domain spaces is the class of Mackey spaces with weakly * sequentially complete dual.Some examples are constructed showing that the class of L_r-spaces is strictly larger than the class of separable B_r-complete spaces.Some properties of L-spaces and L_r-spaces are discussed and the relations between B-complete (resp. B_r-complete) spaces and L-spaces (resp. L_r-spaces) are given.
文摘Let (E,γ) be a locally convex space and E′ its conjugate space. AE′ be an equicontinuous set on (E,γ). In this paper,we show that for each sequence {f i}A and {x j}E, if {x j} converges to 0 in (E,γ), then we can find a f 0∈E′ and extract subsequences {f n i } and {x n j } such that {f n i } converges to f 0 on {x n j } uniformly. If (E,γ) is metrizable,then we can show that the converse is also valid.