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

被引：0
作者：
RuMing Gong
Ji Li
LiXin Yan
机构：
[1] Guangzhou University,School of Mathematics and Information Science
[2] Guangzhou University,Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes
[3] Sun Yat-sen University,Department of Mathematics
来源：
Science China Mathematics | 2013年 / 56卷
关键词：
local Hardy space; non-negative self-adjoint operator; semigroups; local (1, ; )-atoms; Moser type local boundedness condition; space of homogeneous type; 42B30; 42B35; 42B25; 47F05;
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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 L2(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 hL1 (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 hL1(X) can be characterized in terms of the Littlewood-Paley function. Finally, a broad class of applications of these results is described.
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页码：315 / 330
页数：15
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