On superposition of functions of bounded $\phi$-variation
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- by Franciszek Prus-Wiśniowski PDF
- Proc. Amer. Math. Soc. 107 (1989), 361-366 Request permission
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.References
- J. Ciemnoczołowski and W. Orlicz, Composing functions of bounded $\varphi$-variation, Proc. Amer. Math. Soc. 96 (1986), no. 3, 431–436. MR 822434, DOI 10.1090/S0002-9939-1986-0822434-6
- J. Musielak and W. Orlicz, On generalized variations. I, Studia Math. 18 (1959), 11–41. MR 104771, DOI 10.4064/sm-18-1-11-41 F. Prus-Wiśniowski, Some remarks on functions of bounded $\varphi$-variation, Comment. Math. 30 (1991) (to appear).
- L. C. Young, General inequalities for Stieltjes integrals and the convergence of Fourier series, Math. Ann. 115 (1938), no. 1, 581–612. MR 1513204, DOI 10.1007/BF01448958
Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 107 (1989), 361-366
- MSC: Primary 26A45; Secondary 46E30
- DOI: https://doi.org/10.1090/S0002-9939-1989-1011823-8
- MathSciNet review: 1011823