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Traces of Besov and Triebel-Lizorkin spaces on domains

✍ Scribed by Cornelia Schneider

Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
258 KB
Volume
284
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

We determine the trace of Besov spaces \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$\mathfrak {B}^s_{p,q}(\Omega )$\end{document} and Triebel‐Lizorkin spaces \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$\mathfrak {F}^s_{p,q}(\Omega )$\end{document}, characterized via atomic decompositions, on the boundary of C^k^ domains Ω for parameters 0 < p, q ⩽ ∞ and \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$s>\frac{1}{p}$\end{document}. The limiting case \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$s=\frac{1}{p}$\end{document} is investigated as well. In terms of Besov spaces our results remain valid for the classical spaces B^s^~p,q~(Ω) defined via differences. Furthermore, we include some density assertions, which imply that the trace does not exist when \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$s<\frac{1}{p}$\end{document}. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim

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