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On the invariance of classes $\Phi BV, \Lambda BV$ under composition

Author(s): Pamela B. Pierce; Daniel Waterman
Journal: Proc. Amer. Math. Soc. 132 (2004), 755-760.
MSC (2000): Primary 26A45, 42A16
Posted: July 31, 2003
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Abstract: The necessary and sufficient condition for $g \circ f$ to be in the class $\Phi BV, \Lambda BV$ for every $f$ of that class whose range is in the domain of $g$ is that $g$ be in $\operatorname{Lip}1$.

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Additional Information:

Pamela B. Pierce
Affiliation: Department of Mathematics and Computer Science, The College of Wooster, Wooster, Ohio 44691
Email: ppierce@acs.wooster.edu

Daniel Waterman
Affiliation: Department of Mathematics, Florida Atlantic University, Boca Raton, Florida 33431-0991
Email: fourier@earthlink.net

DOI: 10.1090/S0002-9939-03-07129-6
PII: S 0002-9939(03)07129-6
Keywords: Bounded variation, Fourier series
Received by editor(s): October 21, 2002
Posted: July 31, 2003
Communicated by: Andreas Seeger
Copyright of article: Copyright 2003, American Mathematical Society

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