General Besov and Triebel-Lizorkin spaces on domains with irregular boundary are compared with the completion, in those spaces, of the subset of infinitely continuously differentiable functions with compact support in the same domains. It turns out that the set of parameters for which those spaces coincide is strongly related to the fractal dimension of the boundary of the domains.
@article{bwmeta1.element.bwnjournal-article-smv142i1p47bwm,
author = {Ant\'onio Caetano},
title = {Approximation by functions of compact support in Besov-Triebel-Lizorkin spaces on irregular domains},
journal = {Studia Mathematica},
volume = {141},
year = {2000},
pages = {47-63},
zbl = {0985.46019},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv142i1p47bwm}
}
Caetano, António. Approximation by functions of compact support in Besov-Triebel-Lizorkin spaces on irregular domains. Studia Mathematica, Tome 141 (2000) pp. 47-63. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv142i1p47bwm/
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