Composition operators on Lizorkin-Triebel spaces

被引：29
|
作者：
Bourdaud, Gerard [1 ]
Moussai, Madani [2 ]
Sickel, Winfried [3 ]
机构：
[1] Inst Math Jussieu, Equipe Anal Fonct, F-75013 Paris, France
[2] Univ MSila, Dept Math, LMPA, Msila 28000, Algeria
[3] FSU Jena, Math Inst, D-07743 Jena, Germany
来源：
JOURNAL OF FUNCTIONAL ANALYSIS | 2010年 / 259卷 / 05期
关键词：
Composition of functions; Composition operator; Lizorkin-Triebel spaces; Slobodeckij spaces; Bessel potential spaces; Functions of bounded variation; Wiener classes; Optimal inequalities; BOUNDED P-VARIATION; SOBOLEV SPACES; SUPERPOSITION OPERATORS; FUNCTIONAL-CALCULUS; SYMBOLIC-CALCULUS; BESOV ALGEBRAS;
D O I：
10.1016/j.jfa.2010.04.008
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper is devoted to the study of the composition operator Tf(g) := f o g on Lizorkin-Triebel spaces F(p,q)(s)(R). In case s > 1 + (1/p), 1 < p < infinity, and 1 <= q <= infinity we will prove the following; the operator T(f) takes Fq (it) to itself if and only if f(0) = 0 and f belongs locally to fq(111). (C) 2010 Elsevier Inc. All rights reserved.
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页码：1098 / 1128
页数：31
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