On the invariance of certain classes of functions under composition
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- by Milton Chaika and Daniel Waterman PDF
- Proc. Amer. Math. Soc. 43 (1974), 345-348 Request permission
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 $g \in \operatorname {Lip} 1$.References
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Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 43 (1974), 345-348
- MSC: Primary 26A16; Secondary 42A20
- DOI: https://doi.org/10.1090/S0002-9939-1974-0330367-9
- MathSciNet review: 0330367