On the invariance of classes Φ𝐵𝑉,Λ𝐵𝑉 under composition

Pierce, Pamela; Waterman, Daniel

doi:10.1090/S0002-9939-03-07129-6

On the invariance of classes $\Phi BV, \Lambda BV$ under composition
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by Pamela B. Pierce and Daniel Waterman PDF

Proc. Amer. Math. Soc. 132 (2004), 755-760 Request permission

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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