New Properties of Besov and Triebel-Lizorkin Spaces on RD-Spaces - Mathematics > Classical Analysis and ODEsReport as inadecuate




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Abstract: An RD-space $\mathcal X$ is a space of homogeneous type in the sense ofCoifman and Weiss with the additional property that a reverse doubling propertyholds in $\mathcal X$. In this paper, the authors first give several equivalentcharacterizations of RD-spaces and show that the definitions of spaces of testfunctions on $\mathcal X$ are independent of the choice of the regularity$\epsilon\in 0,1$; as a result of this, the Besov and Triebel-Lizorkin spaceson $\mathcal X$ are also independent of the choice of the underlyingdistribution space. Then the authors characterize the norms of inhomogeneousBesov and Triebel-Lizorkin spaces by the norms of homogeneous Besov andTriebel-Lizorkin spaces together with the norm of local Hardy spaces in thesense of Goldberg. Also, the authors obtain the sharp locally integrability ofelements in Besov and Triebel-Lizorkin spaces.



Author: Dachun Yang, Yuan Zhou

Source: https://arxiv.org/



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