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).
@article{243,
title = {The Bi-dimensional space of Korenblum and composition operator},
journal = {Tatra Mountains Mathematical Publications},
volume = {58},
year = {2014},
doi = {10.2478/tatra.v62i0.243},
language = {EN},
url = {http://dml.mathdoc.fr/item/243}
}
Guerrero, J. A.; Merentes, Nelson; Sánchez, J. L. The Bi-dimensional space of Korenblum and composition operator. Tatra Mountains Mathematical Publications, Tome 58 (2014) . doi : 10.2478/tatra.v62i0.243. http://gdmltest.u-ga.fr/item/243/