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

Skrzypczak, Leszek. "Rotation invariant subspaces of Besov and Triebel-Lizorkin space: compactness of embeddings, smoothness and decay of functions.." Revista Matemática Iberoamericana 18.2 (2002): 267-299. <http://eudml.org/doc/39648>.

@article{Skrzypczak2002,
abstract = {Let H be a closed subgroup of the group of rotation of Rn. 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.},
author = {Skrzypczak, Leszek},
journal = {Revista Matemática Iberoamericana},
keywords = {Espacios de Sobolev; Subespacio invariante; Rotación; Compacidad; Inclusiones; Espacios de Holder generalizados; Besov spaces; Triebel-Lizorkin spaces},
language = {eng},
number = {2},
pages = {267-299},
title = {Rotation invariant subspaces of Besov and Triebel-Lizorkin space: compactness of embeddings, smoothness and decay of functions.},
url = {http://eudml.org/doc/39648},
volume = {18},
year = {2002},
}

TY - JOUR
AU - Skrzypczak, Leszek
TI - Rotation invariant subspaces of Besov and Triebel-Lizorkin space: compactness of embeddings, smoothness and decay of functions.
JO - Revista Matemática Iberoamericana
PY - 2002
VL - 18
IS - 2
SP - 267
EP - 299
AB - Let H be a closed subgroup of the group of rotation of Rn. 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.
LA - eng
KW - Espacios de Sobolev; Subespacio invariante; Rotación; Compacidad; Inclusiones; Espacios de Holder generalizados; Besov spaces; Triebel-Lizorkin spaces
UR - http://eudml.org/doc/39648
ER -