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

Wadie Aziz, et al. "A Representation Theorem for $\varphi $-Bounded Variation of Functions in the Sense of Riesz." Commentationes Mathematicae 50.2 (2010): null. <http://eudml.org/doc/292296>.

@article{WadieAziz2010,
abstract = {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].},
author = {Wadie Aziz, Hugo Leiva, Nelson Merentes, Beata Rzepka},
journal = {Commentationes Mathematicae},
keywords = {Bounded variation; function of bounded variation in the sense of Riesz; variations spaces; Banach space; algebra space},
language = {eng},
number = {2},
pages = {null},
title = {A Representation Theorem for $\varphi $-Bounded Variation of Functions in the Sense of Riesz},
url = {http://eudml.org/doc/292296},
volume = {50},
year = {2010},
}

TY - JOUR
AU - Wadie Aziz
AU - Hugo Leiva
AU - Nelson Merentes
AU - Beata Rzepka
TI - A Representation Theorem for $\varphi $-Bounded Variation of Functions in the Sense of Riesz
JO - Commentationes Mathematicae
PY - 2010
VL - 50
IS - 2
SP - null
AB - 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].
LA - eng
KW - Bounded variation; function of bounded variation in the sense of Riesz; variations spaces; Banach space; algebra space
UR - http://eudml.org/doc/292296
ER -