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

Odalis Mejía^*, Nelson Merentes, José Luis Sánchez

Departamento de Matemática, Universidad Central de Venezuela, Caracas, Venezuela.

DOI: 10.4236/apm.2015.511064                

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.

Keywords

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

Conflicts of Interest

The authors declare no conflicts of interest.

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