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Vector valued functions of bounded bidimensional Φ-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 ℝ2, 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. © 2013, Duke University Press. All rights reserved.