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http://hdl.handle.net/10773/15559
Title: | Traces for Besov spaces on fractal h-sets and dichotomy results |
Author: | Caetano, António Haroske, Dorothee |
Keywords: | Fractal h-sets Traces Besov spaces of generalised smoothness Density of test functions Dichotomy |
Issue Date: | 2015 |
Publisher: | Institute of Mathematics of the Polish Academy of Sciences |
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. |
Peer review: | yes |
URI: | http://hdl.handle.net/10773/15559 |
DOI: | 10.4064/sm8171-1-2016 |
ISSN: | 0039-3223 |
Appears in Collections: | CIDMA - Artigos FAAG - Artigos |
Files in This Item:
File | Description | Size | Format | |
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CaHa_arXiv_v2.pdf | Documento principal | 522.43 kB | Adobe PDF | View/Open |
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