by W. Sickel, L. Skrzypczak
Preprint series: 99-20, Analysis
The paper is published: J. Fourier Analysis and Appl., 6 (6), 639-662, 2000.
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