- Tytuł:
- On Bi-dimensional Second Variation
- Autorzy:
-
Ereú, Jurancy
Giménez, José
Merentes, Nelson - Powiązania:
- https://bibliotekanauki.pl/articles/745492.pdf
- Data publikacji:
- 2012
- Wydawca:
- Polskie Towarzystwo Matematyczne
- Tematy:
-
Functions of Bounded Second Variation
Functions of Bounded Variation - Opis:
- 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 \(BV^2 (I_a^b)\).
- Źródło:
-
Commentationes Mathematicae; 2012, 52, 1
0373-8299 - Pojawia się w:
- Commentationes Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł