On the Autonomous Nemytskij Operator in Hölder Spaces | Zendy

Manfred Goebel | Zendy; Frank Sachweh | Zendy

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On the Autonomous Nemytskij Operator in Hölder Spaces

Author(s) -

Manfred Goebel,

Frank Sachweh

Publication year - 1999

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/878

Subject(s) - operator (biology) , mathematics , computer science , chemistry , biochemistry , repressor , transcription factor , gene

The paper is devoted to the autonomous Nemytskij operator (superposition operator) in Holder spaces H 0 [a, b] , (k, a) e x (0, 1]. We study acting, continuity, Lipschitz continuity, and Fréchet differentiability conditions. For k = 0, a E (0, 1] and k e N, a = 1 the respective conditions are both necessary and sufficient. For k E N, a E (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.

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