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- Publisher
- de Gruyter
- Copyright
- © de Gruyter 2009
- ISSN
- 0933-7741
- eISSN
- 1435-5337
- DOI
- 10.1515/FORUM.2009.013
- Publisher site
- See Article on Publisher Site
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.
Journal
Forum Mathematicum – de Gruyter
Published: Mar 1, 2009