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## Traces for Besov spaces on fractal h-sets and dichotomy results

### 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

Topics: Fractal h-sets, Traces, Besov spaces of generalised smoothness, Density of test functions, Dichotomy
Publisher: Institute of Mathematics of the Polish Academy of Sciences
Year: 2015
DOI identifier: 10.4064/sm8171-1-2016
OAI identifier: oai:ria.ua.pt:10773/15559
Journal:

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