On Bi-dimensional Second Variation

Jurancy Ereú, José Giménez, and Nelson Merentes. "On Bi-dimensional Second Variation." Commentationes Mathematicae 52.1 (2012): null. <http://eudml.org/doc/292002>.

@article{JurancyEreú2012,
abstract = {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 $BV^2 (I_a^b)$.},
author = {Jurancy Ereú, José Giménez, Nelson Merentes},
journal = {Commentationes Mathematicae},
keywords = {Functions of Bounded Second Variation; Functions of Bounded Variation},
language = {eng},
number = {1},
pages = {null},
title = {On Bi-dimensional Second Variation},
url = {http://eudml.org/doc/292002},
volume = {52},
year = {2012},
}

TY - JOUR
AU - Jurancy Ereú
AU - José Giménez
AU - Nelson Merentes
TI - On Bi-dimensional Second Variation
JO - Commentationes Mathematicae
PY - 2012
VL - 52
IS - 1
SP - null
AB - 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 $BV^2 (I_a^b)$.
LA - eng
KW - Functions of Bounded Second Variation; Functions of Bounded Variation
UR - http://eudml.org/doc/292002
ER -