Inequalities Involving Essential Norm Estimates of Product-Type Operators

Abstract

Consider an open unit disk D=z∈ℂ:z<1 in the complex plane ℂ, ξ a holomorphic function on D, and ψ a holomorphic self-map of D. For an analytic function f, the weighted composition operator is denoted and defined as follows: Wξ,ψfz=ξzfψz. We estimate the essential norm of this operator from Dirichlet-type spaces to Bers-type spaces and Bloch-type spaces.