We study the existence of traces of Besov spaces on fractal h-sets Γ 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 Γ-there occurs an alternative: either the trace on Γ exists, or smooth functions compactly supported outside Γ are dense in the space. This notion was introduced by Triebel (2008) for the special case of d-sets.
@article{bwmeta1.element.bwnjournal-article-doi-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},
volume = {231},
year = {2015},
pages = {117-147},
zbl = {06545413},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-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) pp. 117-147. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm8171-1-2016/