We consider the notion of p, δ-absolute continuity for functions of several variables introduced in [2] and we investigate the validity of some basic properties that are shared by absolutely continuous functions in the sense of Maly. We introduce the class $δ−BV^p_loc(\Omega,IR^m)$ and we give a characterization of the functions belonging to this class.
DI BARI C, VETRO C (2005). A local notion of absolute continuity in IR^n. RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO, 54(1), 101-108 [10.1007/BF02875747].
A local notion of absolute continuity in IR^n
DI BARI, Cristina;VETRO, Calogero
2005-01-01
Abstract
We consider the notion of p, δ-absolute continuity for functions of several variables introduced in [2] and we investigate the validity of some basic properties that are shared by absolutely continuous functions in the sense of Maly. We introduce the class $δ−BV^p_loc(\Omega,IR^m)$ and we give a characterization of the functions belonging to this class.
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