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Young, L.C. (1937) Sur une généralisation de la notion de variation de pussance piéme bornée au sens de M. Wiener, et sur la convergence des séries de Fourier. Comptes Rendus de l’Académie des Sciences, 204, 470-472.

has been cited by the following article:

• TITLE: The Space of Bounded p(·)-Variation in the Sense Wiener-Korenblum with Variable Exponent

  AUTHORS: O. Mejía, N. Merentes, J. L. Sánchez, M. Valera-López

  KEYWORDS: Generalized Variation, p(·)-Variation in the Sense of Wiener-Korenblum, Exponent Variable, Composition Operator, Matkowski’s Condition

  JOURNAL NAME: Advances in Pure Mathematics, Vol.6 No.1, January 19, 2016

  ABSTRACT: In this paper we present the notion of the space of bounded p(·)-variation in the sense of Wiener-Korenblum with variable exponent. We prove some properties of this space and we show that the composition operator H, associated with , maps the into itself, if and only if h is locally Lipschitz. Also, we prove that if the composition operator generated by maps this space into itself and is uniformly bounded, then the regularization of h is affine in the second variable, i.e. satisfies the Matkowski’s weak condition.