Sierpiński, W. (1933) Sur une propriété des fonctions qui n’ont que des discontinuités de première espèce. Bulletin de la Section Scientifique de l’Académie Roumaine, 16, 1-4.

has been cited by the following article:

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

  AUTHORS: Odalis Mejía, Nelson Merentes, José Luis Sánchez

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

  JOURNAL NAME: Advances in Pure Mathematics, Vol.5 No.11, September 30, 2015

  ABSTRACT: In this paper, we proof some properties of the space of bounded p(·)-variation in Wiener’s sense. We show that a functions is of bounded p(·)-variation in Wiener’s sense with variable exponent if and only if it is the composition of a bounded nondecreasing functions and hölderian maps of the variable exponent. We show that the composition operator H, associated with , maps the spaces 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.