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

作     者：GONG RuMing LI Ji YAN LiXin 

作者机构：School of Mathematics and Information ScienceGuangzhou University Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education InstitutesGuangzhou University Department of MathematicsSun Yat-sen University 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2013年第56卷第2期

页      面：315-330页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

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 

主　　题：local Hardy space non-negative self-adjoint operator semigroups local (1 p)-atoms Moser typelocal boundedness condition space of homogeneous type 

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.