Geodesic
A Representation Theorem for \(\varphi\)-Bounded Variation of Functions in the Sense of Riesz
Commentationes Mathematicae, Tome 50 (2010) no. 2, pp. 109-120.

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In this paper we extend the well known Riesz lemma to the class of bounded \(\varphi\)-variation functions in the sense of Riesz defined on a rectangle \(I_a^b\subset \mathbb{R}^2\). This concept was introduced in [2], where the authors proved that the space \(BV_\varphi^R (I_a^b;\mathbb{R}\) 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].
DOI : 10.14708/cm.v50i2.5177
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, pp.  109-120. doi : 10.14708/cm.v50i2.5177. http://geodesic.mathdoc.fr/articles/10.14708/cm.v50i2.5177/

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