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September, 2006 Superposition operators and functions of bounded $p$-variation
Gérard Bourdaud , Massimo Lanza de Cristoforis , Winfried Sickel
Rev. Mat. Iberoamericana 22(2): 455-487 (September, 2006).

Abstract

We characterize the set of all functions $f$ of $\mathbb R$ to itself such that the associated superposition operator $T_f: g \to f \circ g$ maps the class $BV^1_p (\mathbb R)$ into itself. Here $BV^1_p (\mathbb R)$, $1 \le p < \infty$, denotes the set of primitives of functions of bounded $p$-variation, endowed with a suitable norm. It turns out that such an operator is always bounded and sublinear. Also, consequences for the boundedness of superposition operators defined on Besov spaces $B^s_{p,q}({\mathbb R}^n)$ are discussed.

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Gérard Bourdaud . Massimo Lanza de Cristoforis . Winfried Sickel . "Superposition operators and functions of bounded $p$-variation." Rev. Mat. Iberoamericana 22 (2) 455 - 487, September, 2006.

Information

Published: September, 2006
First available in Project Euclid: 26 October 2006

zbMATH: 1134.46015
MathSciNet: MR2294787

Subjects:
Primary: 46E35 , 47H30

Keywords: boundedness of superposition operators , functions of bounded $p$-variation , homogeneous and inhomogeneous Besov spaces , Peetre's embedding theorem

Rights: Copyright © 2006 Departamento de Matemáticas, Universidad Autónoma de Madrid

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Vol.22 • No. 2 • September, 2006
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