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The Nemitskii Operator in Hölder Spaces: Some Necessary and Sufficient Conditions
Author(s) -
Chiappinelli Raffaele,
Nugari Rita
Publication year - 1995
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/51.2.365
Subject(s) - bounded function , mathematics , operator (biology) , differentiable function , uniform continuity , bounded operator , hölder condition , open set , pure mathematics , mathematical analysis , finite rank operator , discrete mathematics , banach space , metric space , biochemistry , repressor , transcription factor , gene , chemistry
The Nemitskii operator in the Hölder spaces C 0, α (Ω) with Ω an open bounded subset of R n , is studied; necessary and sufficient conditions are given for boundedness, uniform continuity, and uniformly continuous differentiability on bounded sets.