A Representation Theorem for $\varphi $-Bounded Variation of Functions in the Sense of Riesz
Commentationes Mathematicae, Tome 50 (2010) no. 2.

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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 ⊂ 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].
Mots-clés : Bounded variation, function of bounded variation in the sense of Riesz, variations spaces, Banach space, algebra space 
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Wadie Aziz; Hugo Leiva; Nelson Merentes; Beata Rzepka. A Representation Theorem for $\varphi $-Bounded Variation of Functions in the Sense of Riesz. Commentationes Mathematicae, Tome 50 (2010) no. 2. https://geodesic-test.mathdoc.fr/item/COMA_2010__50_2_292296/