Traces of Besov spaces on fractal $h$-sets and dichotomy results
Studia Mathematica, Tome 231 (2015) no. 2, pp. 117-147
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
We study the existence of traces of Besov spaces on fractal $h$-sets $\varGamma $ with a special focus on assumptions necessary for this existence; in other words, we present criteria for the non-existence of traces. In that sense our paper can be regarded as an extension of Bricchi (2004) and a continuation of Caetano (2013). Closely connected with the problem of existence of traces is the notion of dichotomy in function spaces: We can prove that—depending on the function space and the set $\varGamma $—there occurs an alternative: either the trace on $\varGamma $ exists, or smooth functions compactly supported outside $\varGamma $ are dense in the space. This notion was introduced by Triebel (2008) for the special case of $d$-sets.
Keywords:
study existence traces besov spaces fractal h sets vargamma special focus assumptions necessary existence other words present criteria non existence traces sense paper regarded extension bricchi continuation caetano closely connected problem existence traces notion dichotomy function spaces prove depending function space set vargamma there occurs alternative either trace vargamma exists smooth functions compactly supported outside vargamma dense space notion introduced triebel special d sets
Affiliations des auteurs :
António M. Caetano 1 ; Dorothee D. Haroske 2
@article{10_4064_sm8171_1_2016,
author = {Ant\'onio M. Caetano and Dorothee D. Haroske},
title = {Traces of {Besov} spaces on fractal $h$-sets and dichotomy results},
journal = {Studia Mathematica},
pages = {117--147},
publisher = {mathdoc},
volume = {231},
number = {2},
year = {2015},
doi = {10.4064/sm8171-1-2016},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm8171-1-2016/}
}
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%0 Journal Article %A António M. Caetano %A Dorothee D. Haroske %T Traces of Besov spaces on fractal $h$-sets and dichotomy results %J Studia Mathematica %D 2015 %P 117-147 %V 231 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/sm8171-1-2016/ %R 10.4064/sm8171-1-2016 %G en %F 10_4064_sm8171_1_2016
António M. Caetano; Dorothee D. Haroske. Traces of Besov spaces on fractal $h$-sets and dichotomy results. Studia Mathematica, Tome 231 (2015) no. 2, pp. 117-147. doi: 10.4064/sm8171-1-2016
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