|
Description: |
We investigate Besov spaces with positive smoothness, obtained by different approaches. Using an equivalent atomic characterization for these spaces, we are able to study traces in different settings.
The results we obtain are rather complete and extend the ones previously known to small smoothness parameters, that is, when 0
The main theorem states, that, for smoothness s>1/p, the trace space of a Besov space again is a Besov space. Here we also observe the phenomenon, that passing from functions in some source space with integrability p to their traces on hyperplanes of codimension 1 results in a loss of smoothness corresponding to 1/p of a derivative. The limiting case s=1/p is studied as well.
The results extend to more general hyperplanes and smooth boundaries of Ck-domains.
|
