The essential norm of a weighted composition operator on BMOA

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

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