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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Brüdern, Jörg / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Neeb, Karl-Hermann / Noguchi, Junjiro / Shahidi, Freydoon / Sogge, Christopher D. / Wienhard, Anna

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Volume 21, Issue 2 (Jan 2009)

Issues

A difference characterization of Besov and Triebel-Lizorkin spaces on RD-spaces

Detlef Müller
  • Mathematisches Seminar, Christian-Albrechts-Universität Kiel, Ludewig-Meyn-Str. 4, D–24098 Kiel, Germany.
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Dachun Yang
  • Corresponding author
  • School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, People's Republic of China.
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2009-03-12 | DOI: https://doi.org/10.1515/FORUM.2009.013

Abstract

An RD-space 𝒳 is a space of homogeneous type in the sense of Coifman and Weiss with the additional property that a reverse doubling property holds in 𝒳, or equivalently, that there exists a constant a 0 > 1 such that for all x ∈ 𝒳 and 0 < r < diam(𝒳)/a 0, the annulus B(x, a 0 r) \ B(x,r) is nonempty, where diam(𝒳) denotes the diameter of the metric space (𝒳,d). An important class of RD-spaces is provided by Carnot-Carathéodory spaces with a doubling measure. In this paper, the authors introduce some spaces of Lipschitz type on RD-spaces, and discuss their relations with known Besov and Triebel-Lizorkin spaces and various Sobolev spaces. As an application, a difference characterization of Besov and Triebel-Lizorkin spaces on RD-spaces is obtained.

About the article

Received: 2006-12-21

Accepted: 2007-09-12

Published Online: 2009-03-12

Published in Print: 2009-03-01


Citation Information: Forum Mathematicum, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/FORUM.2009.013.

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