Abstract
A Stevic'-Sharma operator denoted by T-psi 1,T-psi 2,T-phi is a generalization product of multiplication, differentiation, and composition operators. In this paper, we characterize the bounded and compact Stevic'-Sharma operator T-psi 1,T-psi 2,T-phi from a general class X of Banach function spaces into Zygmund-type spaces with some of the most convenient test functions on the open unit disk. Using several restrictive terms, we show that all bounded operators T-psi 1,T-psi 2,T-phi from X into the little Zygmund-type spaces are compact. As an application, we show that our results hold up for some other domain spaces of T-psi 1,T-psi 2,T-phi, such as the Hardy space and the weighted Bergman space.