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The composition in multidimensional Triebel–Lizorkin spaces
Author(s) -
Moussai Madani
Publication year - 2011
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200810009
Subject(s) - bounded function , composition (language) , mathematics , space (punctuation) , combinatorics , operator (biology) , mathematical analysis , chemistry , computer science , philosophy , linguistics , biochemistry , repressor , transcription factor , gene , operating system
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