# New Properties of Besov and Triebel-Lizorkin Spaces on RD-Spaces - Mathematics > Classical Analysis and ODEs

New Properties of Besov and Triebel-Lizorkin Spaces on RD-Spaces - Mathematics > Classical Analysis and ODEs - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

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.

Autor: Dachun Yang, Yuan Zhou

Fuente: https://arxiv.org/