Nevanlinna-type characterizations for the bloch space and related spaces

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Abstract

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.

Original languageEnglish
Pages (from-to)123-141
Number of pages19
JournalProceedings of the Edinburgh Mathematical Society
Volume33
Issue number1
DOIs
StatePublished - 1990

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