Compact weighted composition operators on the Hardy space

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