THE BOUNDEDNESS OF OPERATORS ON WEIGHTED MULTI-PARAMETER LOCAL HARDY SPACES

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.

The Local Theory of Completely 1-Summing Mapping Spaces

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 (Ⅱ1(⋅,⋅), π1(⋅)) 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 (Ⅱ1(⋅,⋅), π1(⋅)) if and only if V is finitely representable in {Mn}n∈N in the system (Ⅱ1(⋅,⋅), π1(⋅)). At last, we show that an operator space V is finitely representable in {Mn}n∈N in the system (Ⅱ1(⋅,⋅), π1(⋅)) if and only if V = C.

The Sequence-covering Compact Images of Paracompact Locally Compact Spaces

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.

ON THE PRODUCT OF GTEAUX DIFFERENTIABILITY LOCALLY CONVEX SPACES

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.

Generalized constrained multiobjective games in locally FC-uniform spaces

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.

Almost Fixed Points and Fixed Points of Upper [Lower] Semicontinuous Multimap on Locally G-convex Spaces

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.

Differentiability of Convex Functions in Locally Convex Spaces（Ⅰ）──Continuous Convex Functions and Gateaux Differentiability

ＤｉｆｆｅｒｅｎｔｉａｂｉｌｉｔｙｏｆＣｏｎｖｅｘＦｕｎｃｔｉｏｎｓｉｎＬｏｃａｌｌｙＣｏｎｖｅｘＳｐａｃｅｓ（Ⅰ）──ＣｏｎｔｉｎｕｏｕｓＣｏｎｖｅｘＦｕｎｃｔｉｏｎｓａｎｄＧａｔｅａｕｘＤｉｆｆｅｒｅｎｔｉａｂｉｌｉｔｙＷＵＣｏｎｇｘｉｎＣＨＥＮ...

POINTWISE MULTIPLIERS FOR LOCALIZED MORREY-CAMPANATO SPACES ON RD-SPACES

In this article, the authors characterize pointwise multipliers for localized MorreyCampanato spaces, associated with some admissible functions on RD-spaces, which include localized BMO spaces as a special case. The results obtained are applied to Schrdinger operators and some Laguerre operators.

SOME BEST APPROXIMATION RESULTS IN LOCALLY CONVEX SPACES

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.

The characterization of weighted local hardy spaces on domains and its application

In this paper, we give the four equivalent characterizations for the weighted local hardy spaces on Lipschitz domains. Also, we give their application for the harmonic function defined in bounded Lipschitz domains.

Maximal elements and generalized games involving condensing mappings in locally FC-uniform spaces and applications(Ⅰ)

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.

LOCAL HARDY SPACES ON HEISENBERG GROUP OVER LOCAL FIELDS

Let G be a Heisenberg group over local field K. In the paper we give some local maximal functions which define the Hardy spaces h(P)(G) equivalently, obtain the atomic decomposition of local Hardy spaces. We also give some bounded convolution operators h(P)(G), from which we can characterize h(P)(G) by sqare functions.

GENERALIZED VECTOR QUASI-EQUILIBRIUM PROBLEMSIN LOCALLY G-CONVEX SPACES

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.

POTENTIAL SPACE ESTIMATES IN LOCAL HARDY SPACES FOR GREEN POTENTIALS IN CONVEX DOMAINS

Let Ω be a bounded convex domain in Rn(n≥3) and G(x,y) be the Green function of the Laplace operator -△on Ω Let hPT(Ω) = {f∈D'(Ω) : (?)F ∈ hP(Rn), s.t. F|Ω = f}, by the atom characterization of Local Hardy spaces in a bounded Lipschitz domain, the bound of f Ω(?)2(Gf) for every f ∈hPr(Ω) is obtained, where n/(n + 1) <p≤1.

EQUILIBRIUM EXISTENCE FOR MULTI-LEADER-FOLLOWER GENERALIZED CONSTRAINED MULTIOBJECTIVE GAMES IN LOCALLY FC-UNIFORM SPACES

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.

Systems of generalized vector quasi-variational inclusions and systems of generalized vector quasi-optimization problems in locally FC-uniform spaces

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.

Differentiability of Convex Functions in Locally Convex Spaces(Ⅱ)──Frechet

ＤｉｆｆｅｒｅｎｔｉａｂｉｌｉｔｙｏｆＣｏｎｖｅｘＦｕｎｃｔｉｏｎｓｉｎＬｏｃａｌｌｙＣｏｎｖｅｘＳｐａｃｅｓ（ＩＩ）──ＦｒｅｃｈｅｔＤｉｆｆｅｒｅｎｔｉａｂｉｌｉｔｙＷＵＣｏｎｇｘｉｎＷＡＮＧＸｉａｏｍｉｎＣＨＥＮＧＬｉｘｉｎ吴从ａａａｙ，王晓敏...

ON FULLY CONVEX AND LOCALLY FULLY CONVEX BANACH SPACE*

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.

THE GLOBAL AND LOCAL C^(2)-SOLUTIONS FOR THE WAVE EQUATION □u = G(u_t, Du) IN THREE SPACE DIMENSIONS

Kunio Hidano[4] has shown that the global and local C2-solutions for semilinear wave equations with spherical symmetry in three space dimensions. This paper studies the global and local C2-solutions for the semilinear wave equations without spherical symmetry in three space dimensions. A problem put forward by Hiroyuki Takamura[2] is partially answered.