A local version of Hardy spaces associated with operators on metric spaces  

作　　者：GONG RuMing LI Ji YAN LiXin 

机构地区：[1]School of Mathematics and Information Science,Guangzhou University [2]Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes,Guangzhou University [3]Department of Mathematics,Sun Yat-sen University

出　　处：《Science China Mathematics》2013年第2期315-330,共16页中国科学：数学（英文版）

基　　金：supported by China Postdoctoral Science Foundation funded project(Grant No.201104383);the Fundamental Research Funds for the Central Universities(Grant No.11lGPY56);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

摘　　要：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.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 L2(X).Assume that the semigroup e tL generated by L satisfies the Gaussian upper bounds on L 2(X).In this article we study a local version of Hardy space h1L(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 h1L(X) can be characterized in terms of the Littlewood-Paley function.Finally,a broad class of applications of these results is described.

关 键 词：local Hardy space non-negative self-adjoint operator SEMIGROUPS local （1 p）-atoms Moser typelocal boundedness condition space of homogeneous type 

分 类 号：O177.6[理学—数学]