The notion of a sort of biorthogonal multiple vector-valued bivariate wavelet packets,which are associated with a quantity dilation matrix,is introduced.The biorthogonality property of the multiple vector-valued wavel...The notion of a sort of biorthogonal multiple vector-valued bivariate wavelet packets,which are associated with a quantity dilation matrix,is introduced.The biorthogonality property of the multiple vector-valued wavelet packets in higher dimensions is studied by means of Fourier transform and integral transform biorthogonality formulas concerning these wavelet packets are obtained.展开更多
In this paper, the authors get the Coifman type weighted estimates and weak weighted LlogL estimates for vector-valued generalized commutators of multilinear fractional integral with w ∈ A∞. Furthermore, both the bo...In this paper, the authors get the Coifman type weighted estimates and weak weighted LlogL estimates for vector-valued generalized commutators of multilinear fractional integral with w ∈ A∞. Furthermore, both the boundedness of vector-valued multilinear frac- tional integral and the weak weighted LlogL estimates for vector-valued multilinear fractional integral are also obtained.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
Let φ be an analytic self-map of the complex unit disk and X a Banach space. This paper studies the action of composition operator Cφ: f→foφ on the vector-valued Nevanlinna classes N(X) and Na(X). Certain cri...Let φ be an analytic self-map of the complex unit disk and X a Banach space. This paper studies the action of composition operator Cφ: f→foφ on the vector-valued Nevanlinna classes N(X) and Na(X). Certain criteria for such operators to be weakly compact are given. As a consequence, this paper shows that the composition operator Cφ is weakly compact on N(X) and Na(X) if and only if it is weakly compact on the vector-valued Hardy space H^1 (X) and Bergman space B1(X) respectively.展开更多
If a vector valued function space with a Hausdorff locally convex topology has a property such that every closed strongly bounded subset is compact, then we name this property Helly's property. In this paper, we...If a vector valued function space with a Hausdorff locally convex topology has a property such that every closed strongly bounded subset is compact, then we name this property Helly's property. In this paper, we show a class of vector valued function spaces with Helly's property and consider convergence of vector measures and best approximations in function spaces in this class.展开更多
In this paper,we introduce a new concept,namelyε-arithmetics,for real vectors of any fixed dimension.The basic idea is to use vectors of rational values(called rational vectors)to approximate vectors of real values o...In this paper,we introduce a new concept,namelyε-arithmetics,for real vectors of any fixed dimension.The basic idea is to use vectors of rational values(called rational vectors)to approximate vectors of real values of the same dimension withinεrange.For rational vectors of a fixed dimension m,they can form a field that is an mth order extension Q(α)of the rational field Q whereαhas its minimal polynomial of degree m over Q.Then,the arithmetics,such as addition,subtraction,multiplication,and division,of real vectors can be defined by using that of their approximated rational vectors withinεrange.We also define complex conjugate of a real vector and then inner product and convolutions of two real vectors and two real vector sequences(signals)of finite length.With these newly defined concepts for real vectors,linear processing,such as linear filtering,ARMA modeling,and least squares fitting,can be implemented to real vectorvalued signals with real vector-valued coefficients,which will broaden the existing linear processing to scalar-valued signals.展开更多
This paper concerns with multiple weighted norm inequalities for maximal vector-valued multilinear singular operator and maximal commutators. The Cotlar-type inequality of maximal vector-valued multilinear singular in...This paper concerns with multiple weighted norm inequalities for maximal vector-valued multilinear singular operator and maximal commutators. The Cotlar-type inequality of maximal vector-valued multilinear singular integrals operator is obtained. On the other hand, pointwise estimates for sharp maximal function of two kinds of maximal vector-valued multilinear singular integrals and maximal vector-valued commutators are also established. By the weighted estimates of a class of new variant maximal operator, Cotlar's inequality and the sharp maximal flmction estimates, multiple weighted strong estimates and weak estimates for maximal vector-valued singular integrals of multilinear operators and those for maximal vector-valued commutator of multilinear singular integrals are obtained.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
Dirichlet series with real frequencies which represent entire functions on the complex plane C have been investigated by many authors. Several properties such as topological structures, linear continuous functionals, ...Dirichlet series with real frequencies which represent entire functions on the complex plane C have been investigated by many authors. Several properties such as topological structures, linear continuous functionals, and bases have been considered. Le Hai Khoi derived some results with Dirichlet series having negative real frequencies which represent holomorphic functions in a half plane. In the present paper, we have obtained some properties of holomorphic Dirichlet series having positive exponents, whose coefficients belong to a Banach algebra.展开更多
White and Furukawa have discussed vector-valued Markovian decision programming (VMDP). The relations between finite horizon and infinite horizon about VMDP were discussed in [1]. Furukawa generalized the iteration alg...White and Furukawa have discussed vector-valued Markovian decision programming (VMDP). The relations between finite horizon and infinite horizon about VMDP were discussed in [1]. Furukawa generalized the iteration algorithm from the scalar case into the vector case, and gave the method to find all optimal policies. His algorithm is described briefly in the following way: Starting with any stationary policy, we展开更多
In this paper some new results concerning the C_p classes introduced by Muckenhoupt(1981)and later extended by Sawyer(1983),are provided.In particular,we extend the result to the full expected range p>0,to the weak...In this paper some new results concerning the C_p classes introduced by Muckenhoupt(1981)and later extended by Sawyer(1983),are provided.In particular,we extend the result to the full expected range p>0,to the weak norm,to other operators and to their vector-valued extensions.Some of those results rely upon sparse domination,which in the vector-valued case are provided as well.We will also provide sharp weighted estimates for vector-valued extensions relying on those sparse domination 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.
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
We give in this paper a necessary and sufficient condition of weighted weak and strong type norm inequalities for the vector-valued weighted maximal function.
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
This paper presents a method for seismic vulnerability analysis of bridge structures based on vector-valued intensity measure (viM), which predicts the limit-state capacities efficiently with multi-intensity measure...This paper presents a method for seismic vulnerability analysis of bridge structures based on vector-valued intensity measure (viM), which predicts the limit-state capacities efficiently with multi-intensity measures of seismic event. Accounting for the uncertainties of the bridge model, ten single-bent overpass bridge structures are taken as samples statistically using Latin hypercube sampling approach. 200 earthquake records are chosen randomly for the uncertainties of ground motions according to the site condition of the bridges. The uncertainties of structural capacity and seismic demand are evaluated with the ratios of demand to capacity in different damage state. By comparing the relative importance of different intensity measures, Sa(T1) and Sa(T2) are chosen as viM. Then, the vector-valued fragility functions of different bridge components are developed. Finally, the system-level vulnerability of the bridge based on viM is studied with Duunett- Sobel class correlation matrix which can consider the correlation effects of different bridge components. The study indicates that an increment IMs from a scalar IM to viM results in a significant reduction in the dispersion of fragility functions and in the uncertainties in evaluating earthquake risk. The feasibility and validity of the proposed vulnerability analysis method is validated and the bridge is more vulnerable than any components.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
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
The purpose of this paper is to define the concept of mixed saddle point for a vector-valued Lagrangian of the non-smooth multiobjective vector-valued constrained optimization problem and establish the equivalence of ...The purpose of this paper is to define the concept of mixed saddle point for a vector-valued Lagrangian of the non-smooth multiobjective vector-valued constrained optimization problem and establish the equivalence of the mixed saddle point and an efficient solution under generalized (V, p)-invexity assumptions.展开更多
In this paper, by virtue of separation theorems of convex sets and scalarization functions, some minimax inequalities are first considered. As applications, some existence theorems of vector equilibrium problems with ...In this paper, by virtue of separation theorems of convex sets and scalarization functions, some minimax inequalities are first considered. As applications, some existence theorems of vector equilibrium problems with different order structures were also obtained.展开更多
基金Supported by Natural Science Foundation of Henan Province(0511013500)
文摘The notion of a sort of biorthogonal multiple vector-valued bivariate wavelet packets,which are associated with a quantity dilation matrix,is introduced.The biorthogonality property of the multiple vector-valued wavelet packets in higher dimensions is studied by means of Fourier transform and integral transform biorthogonality formulas concerning these wavelet packets are obtained.
基金Supported by the National Natural Science Foundation of China(11271330,11226104,11226108)the Jiangxi Natural Science Foundation of China(20114BAB211007)the Science Foundation of Jiangxi Education Department(GJJ13703)
文摘In this paper, the authors get the Coifman type weighted estimates and weak weighted LlogL estimates for vector-valued generalized commutators of multilinear fractional integral with w ∈ A∞. Furthermore, both the boundedness of vector-valued multilinear frac- tional integral and the weak weighted LlogL estimates for vector-valued multilinear fractional integral are also obtained.
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Let φ be an analytic self-map of the complex unit disk and X a Banach space. This paper studies the action of composition operator Cφ: f→foφ on the vector-valued Nevanlinna classes N(X) and Na(X). Certain criteria for such operators to be weakly compact are given. As a consequence, this paper shows that the composition operator Cφ is weakly compact on N(X) and Na(X) if and only if it is weakly compact on the vector-valued Hardy space H^1 (X) and Bergman space B1(X) respectively.
文摘If a vector valued function space with a Hausdorff locally convex topology has a property such that every closed strongly bounded subset is compact, then we name this property Helly's property. In this paper, we show a class of vector valued function spaces with Helly's property and consider convergence of vector measures and best approximations in function spaces in this class.
文摘In this paper,we introduce a new concept,namelyε-arithmetics,for real vectors of any fixed dimension.The basic idea is to use vectors of rational values(called rational vectors)to approximate vectors of real values of the same dimension withinεrange.For rational vectors of a fixed dimension m,they can form a field that is an mth order extension Q(α)of the rational field Q whereαhas its minimal polynomial of degree m over Q.Then,the arithmetics,such as addition,subtraction,multiplication,and division,of real vectors can be defined by using that of their approximated rational vectors withinεrange.We also define complex conjugate of a real vector and then inner product and convolutions of two real vectors and two real vector sequences(signals)of finite length.With these newly defined concepts for real vectors,linear processing,such as linear filtering,ARMA modeling,and least squares fitting,can be implemented to real vectorvalued signals with real vector-valued coefficients,which will broaden the existing linear processing to scalar-valued signals.
基金This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 10961015, 11261023, 10871024, 10931001, 11561057) and the Key Laboratory of Mathematics and Complex System, Ministry of Education, China.
文摘This paper concerns with multiple weighted norm inequalities for maximal vector-valued multilinear singular operator and maximal commutators. The Cotlar-type inequality of maximal vector-valued multilinear singular integrals operator is obtained. On the other hand, pointwise estimates for sharp maximal function of two kinds of maximal vector-valued multilinear singular integrals and maximal vector-valued commutators are also established. By the weighted estimates of a class of new variant maximal operator, Cotlar's inequality and the sharp maximal flmction estimates, multiple weighted strong estimates and weak estimates for maximal vector-valued singular integrals of multilinear operators and those for maximal vector-valued commutator of multilinear singular integrals are obtained.
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.
文摘Dirichlet series with real frequencies which represent entire functions on the complex plane C have been investigated by many authors. Several properties such as topological structures, linear continuous functionals, and bases have been considered. Le Hai Khoi derived some results with Dirichlet series having negative real frequencies which represent holomorphic functions in a half plane. In the present paper, we have obtained some properties of holomorphic Dirichlet series having positive exponents, whose coefficients belong to a Banach algebra.
基金Project supported by the National Natural Science Foundation of China.
文摘White and Furukawa have discussed vector-valued Markovian decision programming (VMDP). The relations between finite horizon and infinite horizon about VMDP were discussed in [1]. Furukawa generalized the iteration algorithm from the scalar case into the vector case, and gave the method to find all optimal policies. His algorithm is described briefly in the following way: Starting with any stationary policy, we
基金supported by the Basque Government through the Basque Excellence Research Centre 2018–2021 ProgramAgencia Estatal de Investigacion/European Regional Development Fund of UE(Grant No.MTM 2017-82160-C2-1-P),Acronym“Harmonic Analysis and Quantum Mechanics”+4 种基金Spanish Ministry of Economy and Competitiveness through Basque Center for Applied Mathematics Severo Ochoa Excellence Accreditation(Grant No.SEV-2013-0323)Universidad Nacional del Sur(Grant No.11/X752)Agencia Nacional de Promocion Cientifica y Tecnologica of Argentina(Grant No.PICT 2014-1771)Juan de la Cierva-Formacion2015(Grant No.FJCI-2015-24547)Consejo Nacional de Investigaciones Cientificas y Tecnicas/Proyectos de Investigacion Plurianuales of Argentina(Grant No.11220130100329CO)。
文摘In this paper some new results concerning the C_p classes introduced by Muckenhoupt(1981)and later extended by Sawyer(1983),are provided.In particular,we extend the result to the full expected range p>0,to the weak norm,to other operators and to their vector-valued extensions.Some of those results rely upon sparse domination,which in the vector-valued case are provided as well.We will also provide sharp weighted estimates for vector-valued extensions relying on those sparse domination 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.
文摘We give in this paper a necessary and sufficient condition of weighted weak and strong type norm inequalities for the vector-valued weighted maximal function.
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.
基金National Program on Key Basic Research Project of China(973)under Grant No.2011CB013603National Natural Science Foundation of China under Grant Nos.51378341,91315301Tianjin Municipal Natural Science Foundation under Grant No.13JCQNJC07200
文摘This paper presents a method for seismic vulnerability analysis of bridge structures based on vector-valued intensity measure (viM), which predicts the limit-state capacities efficiently with multi-intensity measures of seismic event. Accounting for the uncertainties of the bridge model, ten single-bent overpass bridge structures are taken as samples statistically using Latin hypercube sampling approach. 200 earthquake records are chosen randomly for the uncertainties of ground motions according to the site condition of the bridges. The uncertainties of structural capacity and seismic demand are evaluated with the ratios of demand to capacity in different damage state. By comparing the relative importance of different intensity measures, Sa(T1) and Sa(T2) are chosen as viM. Then, the vector-valued fragility functions of different bridge components are developed. Finally, the system-level vulnerability of the bridge based on viM is studied with Duunett- Sobel class correlation matrix which can consider the correlation effects of different bridge components. The study indicates that an increment IMs from a scalar IM to viM results in a significant reduction in the dispersion of fragility functions and in the uncertainties in evaluating earthquake risk. The feasibility and validity of the proposed vulnerability analysis method is validated and the bridge is more vulnerable than any components.
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 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The purpose of this paper is to define the concept of mixed saddle point for a vector-valued Lagrangian of the non-smooth multiobjective vector-valued constrained optimization problem and establish the equivalence of the mixed saddle point and an efficient solution under generalized (V, p)-invexity assumptions.
文摘In this paper, by virtue of separation theorems of convex sets and scalarization functions, some minimax inequalities are first considered. As applications, some existence theorems of vector equilibrium problems with different order structures were also obtained.