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

• Autorzy: Wadie Aziz , Hugo Leiva , Nelson Merentes , Beata Rzepka
• Języki publikacji: EN

Abstrakty

EN

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].

Słowa kluczowe

EN

Bounded variation; function of bounded variation in the sense of Riesz; variations spaces; Banach space; algebra space

• Wydawca: Polish Mathematical Society
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2010
• Tom: 50
• Numer: 2

Daty

wydano

2010

online

2017-12-18

Twórcy

autor

Wadie Aziz

autor

Hugo Leiva

autor

Nelson Merentes

autor

Beata Rzepka

Identyfikatory

DOI

10.14708/cm.v50i2.5177