The Spaces of Functions of Two Variables of Bounded κΦ-Variation in the Sense of Schramm-Korenblum

Abstract

The purpose of this paper is twofold. Firstly, we introduce the concept of bounded κΦ-variation in the sense of Schramm-Korenblum for real functions with domain in a rectangle of R2. Secondly, we study some properties of these functions and we prove that the space generated by these functions has a structure of Banach algebra.