The composition in multidimensional Triebel–Lizorkin spaces

We will establish that the composition operator T f : g → f ○ g takes the intersections of Triebel–Lizorkin spaces \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$ F_{{p},{q}}^{s}({\mathbb R}^n) $\end{document} with a certain space of bounded and continuous functions to \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$ F_{{p},{q}}^{s}({\mathbb R}^n) $\end{document} , under some conditions on the parameters n , s , p and q . Also, a similar partial result corresponding to the Besov spaces \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$ B_{{p},{q}}^{s}({{\mathbb R}}^n) $\end{document} will be given. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim