Traces of Besov and Triebel‐Lizorkin spaces on domains

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