On the \(\mathbf {RBV_{(p,\alpha )}^{0}([a,b])}\) variation space as the dual space of \(\mathbf {L_{(p,\alpha )}([a,b])}\)

Abstract

In this paper we study some properties of the space \(RBV_{(p,\alpha )}^{0}([a,b])\). Among other, we proved that the dual space of \(L_{(p,\alpha )}([a,b])\) may be identified with the space \(RBV_{(p,\alpha )}^{0}([a,b])\).