Author(s)

Odalis Mejía¹, Pilar Silvestre², María Valera-López¹

¹Departamento de Matemática, Universidad Central de Venezuela, Caracas, Venezuela.
²University of Barcelona, Spain.

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.

Generalized Variation, De la Vallée Poussin, (p(⋅), 2)-Variation in Wiener’s Sense, Variable Exponent, Composition Operator, Matkowski’s Condition

Mejía, O. , Silvestre, P. and Valera-López, M. (2017) Functions of Bounded (p(⋅), 2)-Variation in De la Vallée Poussin-Wiener’s Sense with Variable Exponent. Advances in Pure Mathematics, 7, 507-532. doi: 10.4236/apm.2017.79033.