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Functional Calculus in Hölder-Zygmund Spaces

G. Bourdaud and Massimo Lanza de Cristoforis
Transactions of the American Mathematical Society
Vol. 354, No. 10 (Oct., 2002), pp. 4109-4129
Stable URL: http://www.jstor.org/stable/3072998
Page Count: 21
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Functional Calculus in Hölder-Zygmund Spaces
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Abstract

In this paper we characterize those functions f of the real line to itself such that the nonlinear superposition operator Tf defined by Tf[g] := fog maps the Hölder-Zygmund space Cs( Rn) to itself, is continuous, and is r times continuously differentiable. Our characterizations cover all cases in which s is real and s > 0, and seem to be novel when s > 0 is an integer.

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