We calculate the essential norm of some extensions of the generalized composition operators between kth weighted-type spaces on the unit disk in the complex plane, considerably extending some results in the literature.

In this paper, we give a new characterization for the boundedness and compactness of differences of generalized weighted composition operators from the Bloch space into weightedtype spaces. Moreover, we give some estimates for the essential norm of these operators. Mathematics subject classification (2010): 30D45, 47B38.

A composition operator is an operator on a space of functions defined on the same set. Its action is by composition to the right with a fixed selfmap of that set. A composition operator followed by a multiplication operator is called a weighted composition operator. In this paper, we study when weighted composition operators on the Hilbert Hardy space of the open unit disc are isometric. We fin...

Let ϕ be a holomorphic self-map and let ψ be a holomorphic function on the unit ball B. The boundedness and compactness of the weighted composition operator ψC ϕ from the generalized weighted Bergman space into a class of weighted-type spaces are studied in this paper.