Besov and Triebel-Lizorkin spaces associated with non-negative self-adjoint operators

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• 作者：Guorong Hu
• 关键词：Besov space ; Triebel&ndash ; Lizorkin space ; Metric measure space ; Heat kernel ; Peetre maximal function ; Atom
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：15 March, 2014
• 年：2014
• 卷：411
• 期：2
• 页码：753-772
• 全文大小：424 K

文摘

Let be a locally compact metric space endowed with a doubling measure 渭, and be a non-negative self-adjoint operator on . Assume that the semigroup generated by consists of integral operators with (heat) kernel enjoying Gaussian upper bound but having no information on the regularity in the variables x and y. In this paper, we introduce Besov and Triebel-Lizorkin spaces associated with , and present an atomic decomposition of these function spaces.