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A Representation Theorem for \(\varphi\)-Bounded Variation of Functions in the Sense of Riesz

100%

Aziz W., Leiva H., Merentes N., Rzepka B.

Commentationes Mathematicae

2010

tom 50

nr 2

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].

Ograniczanie wyników

1 Commentationes Mathematicae

1 Aziz W.

1 Leiva H.

1 Merentes N.

1 Rzepka B.

1 2010

Wyniki wyszukiwania

A Representation Theorem for \(\varphi\)-Bounded Variation of Functions in the Sense of Riesz