Basic properties of nite sum of weighted composition

Abstract

In this paper,we continue the study of nite sum of weighted composi-

tion operators between different Lp-spaces that was investigated by Jabbarzadeh and

Estaremi in 2012. Indeed, we rst obtain some necessary and sufficient conditions for

boundedness of the nite sums of weighted composition operators between distinct

Lp-spaces. In the sequel, we investigate the compactness of nite sum of weighted

composition operators. By using theorems of boundedness and compactness, we esti-

mate the essential norms of these operators. Finally, some examples to illustrate the

main results are given.