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

### Tom 231 / 2015

Studia Mathematica 231 (2015), 117-147 MSC: Primary 46E35; Secondary 28A80. DOI: 10.4064/sm8171-1-2016 Opublikowany online: 18 February 2016

#### Streszczenie

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.

#### Autorzy

• António M. CaetanoCenter for R&D in Mathematics and Applications
Department of Mathematics
University of Aveiro
3810-193 Aveiro, Portugal
e-mail
• Dorothee D. HaroskeInstitute of Mathematics
Friedrich Schiller University Jena
07737 Jena, Germany
e-mail

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