Annals of Functional Analysis

Vector valued functions of bounded bidimensional $\Phi$-variation

Mireya Bracamonte, José Giménez, and Nelson Merente

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Abstract

‎In this article we present a generalization of the concept of‎ ‎function of bounded variation‎, ‎in the sense of Riesz‎, ‎for functions‎ ‎defined on a rectangle in $\mathbb{R}^{2}$‎, ‎which take values in a‎ ‎Banach space‎. ‎As applications‎, ‎we obtain generalizations of some‎ ‎results due to Chistyakov and a counterpart of the classical‎ ‎Riesz's Lemma‎.

Article information

Source
Ann. Funct. Anal., Volume 4, Number 1 (2013), 89-108.

Dates
First available in Project Euclid: 12 May 2014

Permanent link to this document
https://projecteuclid.org/euclid.afa/1399899839

Digital Object Identifier
doi:10.15352/afa/1399899839

Mathematical Reviews number (MathSciNet)
MR3004213

Zentralblatt MATH identifier
1270.26014

Subjects
Primary: 26B30: Absolutely continuous functions, functions of bounded variation
Secondary: 46B20‎ 26B35: Special properties of functions of several variables, Hölder conditions, etc.

Keywords
Bounded variation vector valued function ‎Banach space

Citation

Bracamonte, Mireya; Giménez, José; Merente, Nelson. Vector valued functions of bounded bidimensional $\Phi$-variation. Ann. Funct. Anal. 4 (2013), no. 1, 89--108. doi:10.15352/afa/1399899839. https://projecteuclid.org/euclid.afa/1399899839


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