TITLE:
Functions of Bounded (p(⋅), 2)-Variation in De la Vallée Poussin-Wiener’s Sense with Variable Exponent
AUTHORS:
Odalis Mejía, Pilar Silvestre, María Valera-López
KEYWORDS:
Generalized Variation, De la Vallée Poussin, (p(⋅), 2)-Variation in Wiener’s Sense, Variable Exponent, Composition Operator, Matkowski’s Condition
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.7 No.9,
September
28,
2017
ABSTRACT: In this paper we establish the notion of the space of bounded (p(⋅), 2)variation in De la Vallée Poussin-Wiener’s sense with variable exponent. We show some properties of this space and we show that any uniformly bounded composition operator that maps this space into itself necessarily satisfies the so-called Matkowski’s conditions.