Absolute continuity for Banach space valued mappings

Abstract

We consider the notion of p,λ,δ-absolute continuity for Banach space valued mappings introduced in [2] for real valued functions and for λ = 1. We investigate the validity of some basic properties that are shared by n, λ-absolutely continuous functions in the sense of Maly and Hencl. We introduce the class $δ-BV^p_{λ,loc}$ and we give a characterization of the functions belonging to this class.