Author(s)

O. Mejía^*, N. Merentes, J. L. Sánchez, M. Valera-López

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

In this paper we present the notion of the space of bounded p(·)-variation in the sense of Wiener-Korenblum with variable exponent. We prove some properties of this space and we show that the composition operator H, associated with , maps the  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, i.e. satisfies the Matkowski’s weak condition.

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

Mejía, O. , Merentes, N. , Sánchez, J. and Valera-López, M. (2016) The Space of Bounded p(·)-Variation in the Sense Wiener-Korenblum with Variable Exponent. Advances in Pure Mathematics, 6, 21-40. doi: 10.4236/apm.2016.61004.