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Functional Calculus in Hölder-Zygmund Spaces

Authors:	G Bourdaud Massimo Lanza de Cristoforis

Institution:	Institut de Mathématiques de Jussieu, Équipe d'Analyse Fonctionnelle, Case 186, 4 place Jussieu, 75252 Paris Cedex 05, France ; University of Padova, Dipartimento di Matematica Pura ed Applicata, Via Belzoni 7, 35131 Padova, Italia

Abstract:	In this paper we characterize those functions of the real line to itself such that the nonlinear superposition operator $T_{f}$ defined by $T_{f} g]:= f\circ g$ maps the Hölder-Zygmund space ${\mathcal C}^{s}({\mathbf R}^{n})$ to itself, is continuous, and is times continuously differentiable. Our characterizations cover all cases in which is real and , and seem to be novel when is an integer.

Keywords:	H\"older-Zygmund spaces composition operators

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