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

• Autorzy: António M. Caetano , Dorothee D. Haroske
• Języki publikacji: 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.

Kategorie tematyczne

• 46E35: Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
• 28A80: Fractals

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2015
• Tom: 231
• Numer: 2
• Strony: 117-147

Daty

wydano

2015

Twórcy

autor

António M. Caetano

• Center for R&D in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal

autor

Dorothee D. Haroske

• Institute of Mathematics, Friedrich Schiller University Jena, 07737 Jena, Germany

Identyfikatory

DOI

10.4064/sm8171-1-2016