Traces of Besov and Triebel‐Lizorkin spaces on domains

Abstract

AbstractWe 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 Ck 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 Bsp,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