In this paper, we attempt to give a unified approach to the existing several versions of Ekeland＇s variational principle. In the framework of uniiorm spaces, we introduce p-distances and more generally, q-distances....In this paper, we attempt to give a unified approach to the existing several versions of Ekeland＇s variational principle. In the framework of uniiorm spaces, we introduce p-distances and more generally, q-distances. Then we introduce a new type of completeness for uniform spaces, i.e., sequential completeness with respect to a q-distance （particularly, a p-distance）, which is a very extensive concept of completeness. By using q-distances and the new type of completeness, we prove a generalized Takahashi＇s nonconvex minimization theorem, a generalized Ekeland＇s variational principle and a generalized Caristi＇s fixed point theorem. Moreover, we show that the above three theorems are equivalent to each other. From the generalized Ekeland＇s variational principle, we deduce a number of particular versions of Ekeland＇s principle, which include many known versions of the principle and their improvements.展开更多
In this article, the authors give a typical integral＇s bidirectional estimates for allcases. At the same time, several equivalent characterizations on the F（p, q, s, k） space in theunit ball of Cn are given.
The Hardy space Hpis not locally convex if 0 < p < 1, even though its conjugate space(Hp) separates the points of Hp. But then it is locally p-convex, and its conjugate cone(Hp) p is large enough to separate the...The Hardy space Hpis not locally convex if 0 < p < 1, even though its conjugate space(Hp) separates the points of Hp. But then it is locally p-convex, and its conjugate cone(Hp) p is large enough to separate the points of Hp. In this case, the conjugate cone can be used to replace its conjugate space to set up the duality theory in the p-convex analysis. This paper deals with the representation problem of the conjugate cone(Hp) p of Hpfor 0 < p ≤ 1, and obtains the subrepresentation theorem(Hp) p L∞(T, C p).展开更多
Let （X, d, μ） be a metric measure space endowed with a distance d and a nonnegative Borel doubling measure μ. Let L be a second order self-adjoint positive operator on L^2（X）. Assume that the semigroup e-^tL gen...Let （X, d, μ） be a metric measure space endowed with a distance d and a nonnegative Borel doubling measure μ. Let L be a second order self-adjoint positive operator on L^2（X）. Assume that the semigroup e-^tL generated by -L satisfies the Gaussian upper bounds on L2（X）. In this article we study a local version of Hardy space hi （X） associated with L in terms of the area function characterization, and prove their atomic characters. Furthermore, we introduce a Moser type local boundedness condition for L, and then we apply this condition to show that the space hzL（X） can be characterized in terms of the Littlewood-Paley function. Finally, a broad class of applications of these results is described.展开更多
LetΩ be a bounded symmetric domain in Cn. The purpose of this article is to define and characterize the general function space F（p, q, s） on Ω. Characterizing functions in the F（p, q, s） space is a work of consi...LetΩ be a bounded symmetric domain in Cn. The purpose of this article is to define and characterize the general function space F（p, q, s） on Ω. Characterizing functions in the F（p, q, s） space is a work of considerable interest nowadays. In this article, the authors give several equivalent descriptions of the functions in the F（p, q, s） space on Ω in terms of fractional differential operators. At the same time, the authors give the relationship between F（p, q, s） space and Bloch type space on Ω too.展开更多
基金Supported by National Natural Science Foundation of China(Grant No.10871141)
文摘In this paper, we attempt to give a unified approach to the existing several versions of Ekeland＇s variational principle. In the framework of uniiorm spaces, we introduce p-distances and more generally, q-distances. Then we introduce a new type of completeness for uniform spaces, i.e., sequential completeness with respect to a q-distance （particularly, a p-distance）, which is a very extensive concept of completeness. By using q-distances and the new type of completeness, we prove a generalized Takahashi＇s nonconvex minimization theorem, a generalized Ekeland＇s variational principle and a generalized Caristi＇s fixed point theorem. Moreover, we show that the above three theorems are equivalent to each other. From the generalized Ekeland＇s variational principle, we deduce a number of particular versions of Ekeland＇s principle, which include many known versions of the principle and their improvements.
基金supported by the National Natural Science Foundation of China(11571104)the Hunan Provincial Innovation Foundation for Postgraduate(CX2017B220)Supported by the Construct Program of the Key Discipline in Hunan Province
文摘In this article, the authors give a typical integral＇s bidirectional estimates for allcases. At the same time, several equivalent characterizations on the F（p, q, s, k） space in theunit ball of Cn are given.
基金Supported by the National Natural Science Foundation of China(10671147)Science Foundation of Ministry of Education of China(208081)the Natural Science Foundation of Henan(2008B110006)
基金supported by the National Natural Science Foundation of China(No.10871141)
文摘The Hardy space Hpis not locally convex if 0 < p < 1, even though its conjugate space(Hp) separates the points of Hp. But then it is locally p-convex, and its conjugate cone(Hp) p is large enough to separate the points of Hp. In this case, the conjugate cone can be used to replace its conjugate space to set up the duality theory in the p-convex analysis. This paper deals with the representation problem of the conjugate cone(Hp) p of Hpfor 0 < p ≤ 1, and obtains the subrepresentation theorem(Hp) p L∞(T, C p).
基金supported by China Postdoctoral Science Foundation funded project(Grant No.201104383)the Fundamental Research Funds for the Central Universities(Grant No.11lGPY56)+1 种基金National Natural Science Foundation of China(Grant No.10925106)Guangdong Province Key Laboratory of Computational Science and Grant for Senior Scholars from the Association of Colleges and Universities of Guangdong
文摘Let （X, d, μ） be a metric measure space endowed with a distance d and a nonnegative Borel doubling measure μ. Let L be a second order self-adjoint positive operator on L^2（X）. Assume that the semigroup e-^tL generated by -L satisfies the Gaussian upper bounds on L2（X）. In this article we study a local version of Hardy space hi （X） associated with L in terms of the area function characterization, and prove their atomic characters. Furthermore, we introduce a Moser type local boundedness condition for L, and then we apply this condition to show that the space hzL（X） can be characterized in terms of the Littlewood-Paley function. Finally, a broad class of applications of these results is described.
基金supported by the National Natural Science Foundation of China(11571104)the Hunan Provincial Innovation Foundation for Postgraduate(CX2017B220)Supported by the Construct Program of the Key Discipline in Hunan Province
文摘LetΩ be a bounded symmetric domain in Cn. The purpose of this article is to define and characterize the general function space F（p, q, s） on Ω. Characterizing functions in the F（p, q, s） space is a work of considerable interest nowadays. In this article, the authors give several equivalent descriptions of the functions in the F（p, q, s） space on Ω in terms of fractional differential operators. At the same time, the authors give the relationship between F（p, q, s） space and Bloch type space on Ω too.
