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

Wadie AzizHugo LeivaNelson MerentesBeata 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 2 . This concept was introduced in [2], where the authors proved that the space B V ϕ R ( I a b ; 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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