Weighted composition operators between weak spaces of vector-valued analytic functions

Abstract

Abstract. We consider weighted composition operators W ψ,ϕ : f → ψ(f • ϕ) on spaces of analytic functions on the unit disc, which take values in some complex Banach space. We provide necessary and sufficient conditions for the boundedness and (weak) compactness of W ψ,ϕ on general function spaces, and in particular on weak vector-valued spaces. As an application, we characterize the weak compactness of W ψ,ϕ between two different vector-valued Bloch-type spaces. This result appears to be new also in the scalar-valued case.

Weighted composition operators between Besov-type spaces

“…The proof of this lemma follows by similar lines as in the case of composition operators on Besov spaces ( [12] Boundededness and compactness of the weighted composition operators on spaces of analytic functions has been studied by many authors. For example we refer to [2][3][4][5]9,10,13].…”