A local version of Hardy spaces associated with operators on metric spaces |
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Authors: | RuMing Gong Ji Li LiXin Yan |
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Affiliation: | 1. School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, China 2. Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes, Guangzhou University, Guangzhou, 510006, China 3. Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275, China
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Abstract: | 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 L 2(X). In this article we study a local version of Hardy space h L 1 (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 h L 1 (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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