Compact weighted composition operators on the Hardy space

Abstract

A weighted composition operator C ψ,℘ takes an analytic map f on the open unit disk of the complex plane to the analytic map ψf o ℘, where ℘ is an analytic map of the open unit disk into itself and ψ is an analytic map on the open unit disk. This paper studies how the compactness of C ψ,℘ depends on the interaction between the two maps ψ and ℘.