Let φ and ψ be linear fractional self\|maps of the unit disk D and X a separable Hilbert space. In this paper we completely characterize the weak compactness of the product operators of a composition operation C φ...Let φ and ψ be linear fractional self\|maps of the unit disk D and X a separable Hilbert space. In this paper we completely characterize the weak compactness of the product operators of a composition operation C φ with another one's adjoint C * ψ on the vector\|valued Bergman space B 1(X) for forms C φC * ψ and C * ψC φ.展开更多
In this article, we consider a class of compound vector-valued problem on upper-half plane C＋, which consists of vector Riemann problem along a closed contour in C＋ with matrix coefficient in H61der class and vector...In this article, we consider a class of compound vector-valued problem on upper-half plane C＋, which consists of vector Riemann problem along a closed contour in C＋ with matrix coefficient in H61der class and vector Hilbert problem on the real axis with essential bounded measurable matrix coefficient. Under appropriate assumption we obtain its solution by use of Corona theorem and factorization of matrix functions in decomposed Banach algebras.展开更多
The authors establish operator-valued Fourier multiplier theorems on Triebel spaces on R^N, where the required smoothness of the multiplier functions depends on the dimension N and the indices of the Triebel spaces. T...The authors establish operator-valued Fourier multiplier theorems on Triebel spaces on R^N, where the required smoothness of the multiplier functions depends on the dimension N and the indices of the Triebel spaces. This is used to give a sufficient condition of the maximal regularity in the sense of Triebel spaces for vector-valued Cauchy problems with Dirichlet boundary conditions.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 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
In this paper,the authors obtain the boundedness of vector valued bilinear Calderón-Zygmund operators on products of weighted Herz-Morrey spaces with variable exponents.
In this paper, we obtain that multilinear Calderón-Zygmund operators and their commutators with BMO functions are bounded on products of Herz-Morrey spaces with variable smoothness and integrability. The vector-v...In this paper, we obtain that multilinear Calderón-Zygmund operators and their commutators with BMO functions are bounded on products of Herz-Morrey spaces with variable smoothness and integrability. The vector-valued setting of multilinear Calderón-Zygmund operators is also considered.展开更多
In this article, we study the boundedness of weighted composition operators between different vector-valued Dirichlet spaces. Some sufficient and necessary conditions for such operators to be bounded are obtained exac...In this article, we study the boundedness of weighted composition operators between different vector-valued Dirichlet spaces. Some sufficient and necessary conditions for such operators to be bounded are obtained exactly, which are different completely from the scalar-valued case. As applications, we show that these vector-valued Dirichlet spaces are different counterparts of the classical scalar-valued Dirichlet space and characterize the boundedness of multiplication operators between these different spaces.展开更多
In this paper, we introduce weighted vector-valued Morrey spaces and obtain some estimates for vector-valued commutators on these spaces. Applications to CalderSn-Zygmund singular integral operators, oscillatory singu...In this paper, we introduce weighted vector-valued Morrey spaces and obtain some estimates for vector-valued commutators on these spaces. Applications to CalderSn-Zygmund singular integral operators, oscillatory singular integral operators and parabolic difference equations are considered.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 work,we study the quasilinear initial-boundary value problem , where is a system of real smooth vector fields which is defined on an open domain M of R'', and satisfies the Hormanderls condition,.Assu...in this work,we study the quasilinear initial-boundary value problem , where is a system of real smooth vector fields which is defined on an open domain M of R'', and satisfies the Hormanderls condition,.Assume that is non characteristic for the system X,,..',Xm. Under some hypothesis for the boundary of domain and the elliptic structure condition for nonlinear coerfficients Aij, Bj, C,(i, j= 1, ..', m), we have proved that the existence and regularity of solution for aboveinitialboudary value problems.展开更多
In the framework of Frechet spaces, we give a generalized vector-valued Ekeland＇s variational principle, where the perturbation involves the subadditive functions of countable generating semi-norms. By modifying and ...In the framework of Frechet spaces, we give a generalized vector-valued Ekeland＇s variational principle, where the perturbation involves the subadditive functions of countable generating semi-norms. By modifying and developing the method of Cammaroto and Chinni, we obtain a density theorem on extremal points of the vector-valued variational principle, which extends and improves the related known results.展开更多
In this article, we extend the well known Wendel＇s theorem to the context of vector-valued L1-spaces on hypergroups. In this regard, various cases have been studied.
We establish operator-valued Fourier multiplier theorems on periodic Triebel spaces, where the required smoothness of the multipliers depends on the indices of the Triebel spaces. This is used to give a characterizati...We establish operator-valued Fourier multiplier theorems on periodic Triebel spaces, where the required smoothness of the multipliers depends on the indices of the Triebel spaces. This is used to give a characterization of the maximal regularity in the sense of Triebel spaces for Cauchy problems with periodic boundary conditions.展开更多
文摘Let φ and ψ be linear fractional self\|maps of the unit disk D and X a separable Hilbert space. In this paper we completely characterize the weak compactness of the product operators of a composition operation C φ with another one's adjoint C * ψ on the vector\|valued Bergman space B 1(X) for forms C φC * ψ and C * ψC φ.
基金supported by the National Natural Science Foundation of China(10471107)RFDP of Higher Education(20060486001)
文摘In this article, we consider a class of compound vector-valued problem on upper-half plane C＋, which consists of vector Riemann problem along a closed contour in C＋ with matrix coefficient in H61der class and vector Hilbert problem on the real axis with essential bounded measurable matrix coefficient. Under appropriate assumption we obtain its solution by use of Corona theorem and factorization of matrix functions in decomposed Banach algebras.
文摘The authors establish operator-valued Fourier multiplier theorems on Triebel spaces on R^N, where the required smoothness of the multiplier functions depends on the dimension N and the indices of the Triebel spaces. This is used to give a sufficient condition of the maximal regularity in the sense of Triebel spaces for vector-valued Cauchy problems with Dirichlet boundary conditions.
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.
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(Nos.11761026)Guangxi Natural Science Foundation(No.2020GXNSFAA159085)。
文摘In this paper,the authors obtain the boundedness of vector valued bilinear Calderón-Zygmund operators on products of weighted Herz-Morrey spaces with variable exponents.
基金The NSF(11361020)of Chinathe NSF(20151011)of Hainan Province
文摘In this paper, we obtain that multilinear Calderón-Zygmund operators and their commutators with BMO functions are bounded on products of Herz-Morrey spaces with variable smoothness and integrability. The vector-valued setting of multilinear Calderón-Zygmund operators is also considered.
基金supported by the National Natural Science Foundation of China (10901158)
文摘In this article, we study the boundedness of weighted composition operators between different vector-valued Dirichlet spaces. Some sufficient and necessary conditions for such operators to be bounded are obtained exactly, which are different completely from the scalar-valued case. As applications, we show that these vector-valued Dirichlet spaces are different counterparts of the classical scalar-valued Dirichlet space and characterize the boundedness of multiplication operators between these different spaces.
基金Supported by National Natural Science Foundation of China(Grant Nos.10901076and11271175)National Natural Science Foundation of Shandong Province(Grant No.ZR2012AQ026)the Key Laboratory of Mathematics and Complex System (Beijing Normal University),Ministry of Education,China
文摘In this paper, we introduce weighted vector-valued Morrey spaces and obtain some estimates for vector-valued commutators on these spaces. Applications to CalderSn-Zygmund singular integral operators, oscillatory singular integral operators and parabolic difference equations are considered.
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.
文摘in this work,we study the quasilinear initial-boundary value problem , where is a system of real smooth vector fields which is defined on an open domain M of R'', and satisfies the Hormanderls condition,.Assume that is non characteristic for the system X,,..',Xm. Under some hypothesis for the boundary of domain and the elliptic structure condition for nonlinear coerfficients Aij, Bj, C,(i, j= 1, ..', m), we have proved that the existence and regularity of solution for aboveinitialboudary value problems.
基金Supported by National Natural Science Foundation of China (Grant No.10871141)
文摘In the framework of Frechet spaces, we give a generalized vector-valued Ekeland＇s variational principle, where the perturbation involves the subadditive functions of countable generating semi-norms. By modifying and developing the method of Cammaroto and Chinni, we obtain a density theorem on extremal points of the vector-valued variational principle, which extends and improves the related known results.
基金supported by senior research fellowship of CSIR,India
文摘In this article, we extend the well known Wendel＇s theorem to the context of vector-valued L1-spaces on hypergroups. In this regard, various cases have been studied.
基金The first author is supported by the NSF of China the Excellent Young Teachers Program of MOE,P.R.C.
文摘We establish operator-valued Fourier multiplier theorems on periodic Triebel spaces, where the required smoothness of the multipliers depends on the indices of the Triebel spaces. This is used to give a characterization of the maximal regularity in the sense of Triebel spaces for Cauchy problems with periodic boundary conditions.
