A difference characterization of Besov and Triebel-Lizorkin spaces on RD-spaces
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Detlef Müller
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 a0 > 1 such that for all x ∈ 𝒳 and 0 < r < diam(𝒳)/a0, the annulus B(x, a0r) \ 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.
© de Gruyter 2009
Articles in the same Issue
- Homotopy theory of small diagrams over large categories
- A classification of transitive ovoids, spreads, and m-systems of polar spaces
- Frobenius complements of exponent dividing 2m · 9
- Asymptotics of class numbers for progressions and for fundamental discriminants
- A difference characterization of Besov and Triebel-Lizorkin spaces on RD-spaces
- A topological version of the Bergman property
- A unified treatment of certain majorization results on eigenvalues and singular values of matrices
- Finite index subgroups of conjugacy separable groups
- A Bohr-like compactification and summability of Fourier series
Articles in the same Issue
- Homotopy theory of small diagrams over large categories
- A classification of transitive ovoids, spreads, and m-systems of polar spaces
- Frobenius complements of exponent dividing 2m · 9
- Asymptotics of class numbers for progressions and for fundamental discriminants
- A difference characterization of Besov and Triebel-Lizorkin spaces on RD-spaces
- A topological version of the Bergman property
- A unified treatment of certain majorization results on eigenvalues and singular values of matrices
- Finite index subgroups of conjugacy separable groups
- A Bohr-like compactification and summability of Fourier series
