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.
DI BARI C, VETRO C (2007). Absolute continuity for Banach space valued mappings. RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO, 56, 116-124.
Absolute continuity for Banach space valued mappings
DI BARI, Cristina;VETRO, Calogero
2007-01-01
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.
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