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Composition operators on Lizorkin-Triebel spaces |
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| Authors: | Gé rard Bourdaud,Madani Moussai |
| Affiliation: | a Institut de Mathématiques de Jussieu, Équipe d'analyse fonctionnelle, 175 rue du Chevaleret, 75013 Paris, France b Department of Mathematics, LMPA, University of M'Sila, P.O. Box 166, 28000 M'Sila, Algeria c Mathematisches Institut, FSU Jena, Ernst-Abbe-Platz 1-2, O7743 Jena, Germany |
| Abstract: | This paper is devoted to the study of the composition operator Tf(g):=f○g on Lizorkin-Triebel spaces  . In case s>1+(1/p), 1<p<∞, and 1?q?∞ we will prove the following: the operator Tf takes  to itself if and only if f(0)=0 and f belongs locally to  . |
| Keywords: | Composition of functions Composition operator Lizorkin-Triebel spaces Slobodeckij spaces Bessel potential spaces Functions of bounded variation Wiener classes Optimal inequalities |
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