Essential norm estimates for composition operators on BMOA

We provide two function-theoretic estimates for the essential norm of a composition operator Cφ acting on the space BMOA; one in terms of the n-th power φn of the symbol φ and one which involves the Nevanlinna counting function. We also show that if the symbol φ is univalent, then the essential norm of Cφ is comparable to its essential norm on the Bloch space.