Zeitschrift für Analysis und ihre Anwendungen Vol. 18, No. 2, pp. 205  229 (1999) 

On the Autonomous Nemytskij Operator in Hölder SpacesM. Goebel and F. SachwehM. Goebel: MartinLutherUniversität HalleWittenberg, FB Math. und Inform., D06099 Halle (Saale); goebel@mathematik.unihalle.deF. Sachweh: Bispinckpl. 13, D48683 Ahaus; f_sachweh@lauder.de Abstract: The paper is devoted to the autonomous Nemytskij operator (superposition operator) in Hölder spaces $H^{k+\alpha}[a,b]$, $(k,\alpha) \in \Bbb{Z}_+ \times (0,1]$. We study acting, continuity, Lipschitz continuity, and Fréchet differentiability conditions. For $k = 0$, $\alpha \in (0,1]$ and $k \in \Bbb{N}$, $\alpha = 1$ the respective conditions are both necessary and sufficient. For $k \in \Bbb{N}$, $\alpha \in (0,1)$ only the acting condition is both necessary and sufficient; the other investigated properties are characterized by necessary and sufficient conditions different from each other. Keywords: Hölder spaces, Lipschitz spaces, Nemytskij operator, superposition operator, acting conditions, boundedness, continuity and Lipschitz continuity, Fréchet differentiability Full text of the article:
Electronic fulltext finalized on: 31 Jul 2001. This page was last modified: 9 Nov 2001.
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