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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the invariance of certain classes of functions under composition


Authors: Milton Chaika and Daniel Waterman
Journal: Proc. Amer. Math. Soc. 43 (1974), 345-348
MSC: Primary 26A16; Secondary 42A20
MathSciNet review: 0330367
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Abstract: Certain classes of functions are mapped into themselves by any change of variable. For some classes of this type which are of interest in the study of Fourier series, it is shown that the necessary and sufficient condition that $ g \circ f$ be in the class for each $ f$ of that class is that $ g \in \operatorname{Lip} 1$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0330367-9
PII: S 0002-9939(1974)0330367-9
Keywords: Lipschitz classes, compositions, convergence of Fourier series, generalized bounded variation
Article copyright: © Copyright 1974 American Mathematical Society