In this paper we characterize those functions $f$ of the real line to itself, such that the nonlinear superposition operator $T_{f}$ defined by $T_{f}[ g]:= f\circ g$ maps the H\"older-Zygmund space $\HSn{s}$ 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 in case $s>0$ is integer.
Functional Calculus in Hoelder-Zygmund Spaces
LANZA DE CRISTOFORIS, MASSIMO
2002
Abstract
In this paper we characterize those functions $f$ of the real line to itself, such that the nonlinear superposition operator $T_{f}$ defined by $T_{f}[ g]:= f\circ g$ maps the H\"older-Zygmund space $\HSn{s}$ 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 in case $s>0$ is integer.File in questo prodotto:
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