%0 Journal Article %T The Space of Bounded p(·)-Variation in Wiener’s Sense with Variable Exponent %A Odalis Mejía %A Nelson Merentes %A José Luis Sánchez %J Advances in Pure Mathematics %P 703-716 %@ 2160-0384 %D 2015 %I Scientific Research Publishing %R 10.4236/apm.2015.511064 %X 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. %K Generalized Variation %K p(& %K #183 %K )-Variation in Wiener’s Sense %K Variable Exponent %K Composition Operator %K Matkowski’s Condition %U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=60093