Compact weighted composition operators on the Hardy space

A weighted composition operator $C_{\psi,\varphi}$ takes an analytic map $f$ on the open unit disk of the complex plane to the analytic map $\psi f\circ \varphi$, where $\varphi$ 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 $C_{\psi,\varphi}$ depends on the interaction between the two maps $\psi$ and $\varphi$.