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.