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• # Artykuł - szczegóły

## Studia Mathematica

2015 | 231 | 2 | 117-147

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

EN

### Abstrakty

EN
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.

117-147

wydano
2015

### Twórcy

autor
• Center for R&D in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
autor
• Institute of Mathematics, Friedrich Schiller University Jena, 07737 Jena, Germany