TITLE:
Locally Defined Operators and Locally Lipschitz Composition Operators in the Space WBVp(·)([a, b])
AUTHORS:
José Atilio Guerrero, Odalis Mejía, Nelson Merentes
KEYWORDS:
Generalized Variation, p(·)-Variation in Wiener’s Sense, Variable Exponent, Convergence, Helly’s Theorem, Local Operator
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.6 No.10,
September
27,
2016
ABSTRACT: We give a neccesary and sufficient condition on a functionsuch that the composition operator (Nemytskij Operator) H defined by acts in the space and satisfies a local Lipschitz condition. And, we prove that every locally defined operator mapping the space of continuous and bounded Wiener p(·)-variation with variable exponent functions into itself is a Nemytskij com-position operator.