# On Bi-dimensional Second Variation

Jurancy Ereú; José Giménez; Nelson Merentes

Commentationes Mathematicae (2012)

- Volume: 52, Issue: 1
- ISSN: 2080-1211

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topJurancy 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 -

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