Nevanlinna-type characterizations for the bloch space and related spaces

We give a characterisation of the Bloch space in terms of an area version of the Nevanlinna characteristic, analogous to Baernstein's description of the space BMOA in terms of the usual Nevanlinna characteristic. We prove analogous results for the little Bloch space and the space VMOA, and give value distribution characterizations for all these spaces. Finally we give valence conditions on a Bloch or little Bloch function for containment in BMOA or VMOA.