Radial subspaces of Besov and Lizorkin-Triebel classes: Extended strauss lemma and compactness of embeddings

• DOI: 10.1007/bf02510700
• Publication Date: 2006-10-11T11:28:50Z
• Authors: Winfried Sickel; Leszek Skrzypczak
• Keywords: Lemma (botany); Smoothness; Infinity

In this article, 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 of an adapted atomic decomposition.