Traces for Besov spaces on fractal h-sets and dichotomy results
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...
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | article |
| Language: | eng |
| Published: |
2016
|
| Subjects: | |
| Online Access: | http://hdl.handle.net/10773/15559 |
| Country: | Portugal |
| Oai: | oai:ria.ua.pt:10773/15559 |
| Summary: | 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. |
|---|