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June, 2002 Rotation invariant subspaces of Besov and Triebel-Lizorkin space: compactness of embeddings, smoothness and decay of functions
Leszek Skrzypczak
Rev. Mat. Iberoamericana 18(2): 267-299 (June, 2002).

Abstract

Let $H$ be a closed subgroup of the group of rotation of $\mathbb{R}^n$. The subspaces of distributions of Besov-Lizorkin-Triebel type invariant with respect to natural action of $H$ are investigated. We give sufficient and necessary conditions for the compactness of the Sobolev-type embeddings. It is also proved that $H$-invariance of function implies its decay properties at infinity as well as the better local smoothness. This extends the classical Strauss lemma. The main tool in our investigations is an adapted atomic decomposition.

Citation

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Leszek Skrzypczak. "Rotation invariant subspaces of Besov and Triebel-Lizorkin space: compactness of embeddings, smoothness and decay of functions." Rev. Mat. Iberoamericana 18 (2) 267 - 299, June, 2002.

Information

Published: June, 2002
First available in Project Euclid: 28 April 2003

zbMATH: 1036.46028
MathSciNet: MR1949829

Subjects:
Primary: 42C15, 46E35

Rights: Copyright © 2002 Departamento de Matemáticas, Universidad Autónoma de Madrid

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Vol.18 • No. 2 • June, 2002
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