The essential norm of a weighted composition operator on BMOA

Abstract

We consider weighted composition operators \({W_{\psi ,\varphi }}:f\mapsto \psi (f\circ \varphi )\) on the space BMOA, which consists of the analytic functions on the unit disc whose boundary values have bounded mean oscillation on the unit circle. We provide an estimate for the essential norm of \({W_{\psi ,\varphi }}\) in terms of the weight function \(\psi \) and the \(n\)-th power \(\varphi ^n\) of the analytic self-map \(\varphi \) of the open unit disc. We also provide a new estimate for the norm of \({W_{\psi ,\varphi }}\).