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A Representation Theorem for $ϕ$ -Bounded Variation of Functions in the Sense of Riesz

Wadie Aziz; Hugo Leiva; Nelson Merentes; Beata Rzepka — 2010

Commentationes Mathematicae

In this paper we extend the well known Riesz lemma to the class of bounded $ϕ$ -variation functions in the sense of Riesz defined on a rectangle $I_{a}^{b} \subset ℝ^{2}$ . This concept was introduced in [2], where the authors proved that the space $B V_{ϕ}^{R} (I_{a}^{b}; ℝ$ of such functions is a Banach Algebra. Moreover, they characterized also the Nemytskii operator acting in this space. Thus our result creates a continuation of the paper [2].

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