Upper and Lower Bounds for Essential Norm of Weighted Composition Operators from Bergman Spaces with Békollé Weights

Abstract

Let σ be a weight function such that σ/1−z2α is in the class Bp0α of Békollé weights, μ a normal weight function, ψ a holomorphic map on D, and φ a holomorphic self-map on D. In this paper, we give upper and lower bounds for essential norm of weighted composition operator Wψ,φ acting from weighted Bergman spaces Apσ to Bloch-type spaces Bμ.