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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On superposition of functions of bounded $\phi$-variation

Author: Franciszek Prus-Wiśniowski
Journal: Proc. Amer. Math. Soc. 107 (1989), 361-366
MSC: Primary 26A45; Secondary 46E30
MathSciNet review: 1011823
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Abstract: J. Ciemnoczolowski and W. Orlicz in [1] have obtained some results concerning superpositions of functions of bounded $\varphi$-variation. In this note we show that the assumption in Theorem 1 of [1] that if $\psi$ satisfies ${\Delta _2}$ condition may be dropped. Moreover, Theorem 2.B of [1] is extended to a stronger version.

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Keywords: Function of bounded <IMG WIDTH="19" HEIGHT="37" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="$\varphi$">-variation, composition, generalized Lipschitz condition
Article copyright: © Copyright 1989 American Mathematical Society