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.
Publié le : 2002-03-14
Classification:
Compact embeddings,
Besov and Lizorkin-Triebel spaces,
atomic decompositions,
46E35,
42C15
@article{1051544238,
author = {Skrzypczak, Leszek},
title = {Rotation invariant subspaces of Besov and Triebel-Lizorkin
space: compactness of embeddings, smoothness and decay of functions},
journal = {Rev. Mat. Iberoamericana},
volume = {18},
number = {1},
year = {2002},
pages = { 267-299},
language = {en},
url = {http://dml.mathdoc.fr/item/1051544238}
}
Skrzypczak, Leszek. Rotation invariant subspaces of Besov and Triebel-Lizorkin
space: compactness of embeddings, smoothness and decay of functions. Rev. Mat. Iberoamericana, Tome 18 (2002) no. 1, pp. 267-299. http://gdmltest.u-ga.fr/item/1051544238/