The essential norm of a weighted composition operator on BMOA

Abstract

We provide an estimate for the essential norm of a weighted composition operator $W_{\psi ,\phi }:f\mapsto \psi (f\circ \phi )$ acting on the space $BMOA$ in terms of the weight function $\psi$ and the $n$-th power ${\phi }^n$ of the analytic self-map $\phi$ of the open unit disc $\mathbb{D}$. We also provide a new estimate for the norm of the weighted composition operator on $BMOA$.