The Essential Norm of a Generalized Composition Operator Between Bloch-Type Spaces and Q K Type Spaces

Abstract

Let φ be an analytic self-map of the unit disk \({\rm \mathbb{D},H(\rm \mathbb{D})}\) the space of analytic functions on \({{\rm \mathbb{D}}}\) and \({g \in H(\rm \mathbb{D})}\). We define a linear operator as follows $$C_\varphi^gf(z)=\int\limits_0^zf'(\varphi(w))g(w)\, {\rm d}w, $$ on \({ H(\rm \mathbb{D})}\). In this paper, estimates for the essential norm of the generalized composition operator between Bloch-type spaces and QK type spaces are obtained.