Traces of Besov spaces on fractal h-sets and dichotomy results

António M. Caetano, and Dorothee D. Haroske. "Traces of Besov spaces on fractal h-sets and dichotomy results." Studia Mathematica 231.2 (2015): 117-147. <http://eudml.org/doc/285465>.

@article{AntónioM2015,
abstract = {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.},
author = {António M. Caetano, Dorothee D. Haroske},
journal = {Studia Mathematica},
keywords = {fractal $h$-sets; traces; Besov spaces of generalized smoothness; density of test functions; dichotomy},
language = {eng},
number = {2},
pages = {117-147},
title = {Traces of Besov spaces on fractal h-sets and dichotomy results},
url = {http://eudml.org/doc/285465},
volume = {231},
year = {2015},
}

TY - JOUR
AU - António M. Caetano
AU - Dorothee D. Haroske
TI - Traces of Besov spaces on fractal h-sets and dichotomy results
JO - Studia Mathematica
PY - 2015
VL - 231
IS - 2
SP - 117
EP - 147
AB - 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.
LA - eng
KW - fractal $h$-sets; traces; Besov spaces of generalized smoothness; density of test functions; dichotomy
UR - http://eudml.org/doc/285465
ER -