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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 classes $\Phi BV, \Lambda BV$ under composition


Authors: Pamela B. Pierce and Daniel Waterman
Journal: Proc. Amer. Math. Soc. 132 (2004), 755-760
MSC (2000): Primary 26A45, 42A16
Published electronically: July 31, 2003
MathSciNet review: 2019952
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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: http://dx.doi.org/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
Published electronically: July 31, 2003
Communicated by: Andreas Seeger
Article copyright: © Copyright 2003 American Mathematical Society