On Stević-Sharma Operators from General Class of Analytic Function Spaces into Zygmund-Type Spaces - M. A. Bakhit; A. Kamal (Journal of Function Spaces)
A Stevic′-Sharma operator denoted by Tψ1,ψ2,φ is a generalization product of multiplication, differentiation, and composition operators. In this paper, we characterize the bounded and compact Stevic′-Sharma operator Tψ1,ψ2,φ 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 Tψ1,ψ2,φ 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 Tψ1,ψ2,φ, such as the Hardy space and the weighted Bergman space.