On Bi-dimensional Second Variation

• Autorzy: Jurancy Ereú , José Giménez , Nelson Merentes
• Języki publikacji: EN

Abstrakty

EN

In this paper we present the concept of bounded second variation of a real valued function defined on a rectangle in \(\mathbb{R}^2\). We use Hardy-Vitali type technics in the plane in order to extend the classical notion of function of bounded second variation on intervals of \(\mathbb{R}\). We introduce the class \(BV^2(I_a^b )\), of all functions of bounded second variation on a rectangle \(I_a^b \subset \mathbb{R}^2\), and show that this class can be equipped with a norm with respect to which it is a Banach space. Finally, we present two results that show that integrals of functions of first bounded variation (on \(I_a^b\)) are in \(BV^2 (I_a^b)\).

Słowa kluczowe

EN

Functions of Bounded Second Variation; Functions of Bounded Variation

• Wydawca: Polish Mathematical Society
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2012
• Tom: 52
• Numer: 1

Daty

wydano

2012

online

2017-12-19

Twórcy

autor

Jurancy Ereú

autor

José Giménez

autor

Nelson Merentes

Identyfikatory

DOI

10.14708/cm.v52i1.5326