Vector valued functions of bounded bidimensional $\Phi$-variation

Abstract

‎In this article we present a generalization of the concept of‎ ‎function of bounded variation‎, ‎in the sense of Riesz‎, ‎for functions‎ ‎defined on a rectangle in $\mathbb{R}^{2}$‎, ‎which take values in a‎ ‎Banach space‎. ‎As applications‎, ‎we obtain generalizations of some‎ ‎results due to Chistyakov and a counterpart of the classical‎ ‎Riesz's Lemma‎.