Radial subspaces of Besov and Lizorkin-Triebel classes; extended Strauss lemma and compactness of embeddings

by    W. Sickel, L. Skrzypczak

Preprint series: 99-20, Analysis

The paper is published: J. Fourier Analysis and Appl., 6 (6), 639-662, 2000.

46E35 Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
42C15 Series of general orthogonal functions, generalized Fourier expansions, nonorthogonal expansions

Abstract: In this paper the subspaces of radial distributions of Besov-Lizorkin-Triebel type are investigated. We give sufficient and necessary conditions for the compactness of the Sobolev-type embeddings.
It is also proved that smoothness of the radial function implies decay of the function at infinity. This extends the classical Strauss lemma.
The main tool in our investigations consists in an adapted atomic decomposition.

Keywords: radial distribution, Besov and Lizorkin-Triebel spaces, compact embeddings, atomic decompositions

Upload: 1999-03-15

Update: 2001-04-06

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