The Bi-dimensional space of Korenblum and composition operator

Abstract

In this paper we present the concept of total -$...$-variation in the sense of Hardy-Vitali-Korenblum for real function defined in the rectangle $...$. We show that the space $...$ of the real function, of two variable with finite total $...$-variation is a Banach space endowed with the norm $...$.  Also, we characterize the Nemytskij composition operator $H$ that map the space of two real variable of bounded $...$-variation $...$ into another space of a similar type and is uniformly bounded (or Lipschitzian or uniformly continuous).