JournalsrmiVol. 18, No. 2pp. 267–299

Rotation invariant subspaces of Besov and Triebel-Lizorkin space: compactness of embeddings, smoothness and decay of functions

  • Leszek Skrzypczak

    Adam Mickiewicz University, Poznan, Poland
Rotation invariant subspaces of Besov and Triebel-Lizorkin space: compactness of embeddings, smoothness and decay of functions cover
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Abstract

Let HH be a closed subgroup of the group of rotation of Rn\mathbb{R}^n. The subspaces of distributions of Besov-Lizorkin-Triebel type invariant with respect to natural action of HH are investigated. We give sufficient and necessary conditions for the compactness of the Sobolev-type embeddings. It is also proved that HH-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.

Cite this article

Leszek Skrzypczak, Rotation invariant subspaces of Besov and Triebel-Lizorkin space: compactness of embeddings, smoothness and decay of functions. Rev. Mat. Iberoam. 18 (2002), no. 2, pp. 267–299

DOI 10.4171/RMI/319