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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 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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1989-1011823-8
PII: S 0002-9939(1989)1011823-8
Keywords: Function of bounded $ \varphi $-variation, composition, generalized Lipschitz condition
Article copyright: © Copyright 1989 American Mathematical Society