On functions in the little Bloch space
and inner functions
Abstract: We prove that analytic functions in the little Bloch space assume every value as a radial limit on a set of Hausdorff dimension one, unless they have radial limits on a set of positive measure. The analogue for inner functions in the little Bloch space is also proven, and characterizations of various classes of Bloch functions in terms of their level sets are given.
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Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109; Fachbereich Mathematik, TU Berlin, 10623 Berlin, Germany
Received by editor(s): June 10, 1994
Additional Notes: Research performed in part as a Feodor Lynen Fellow of the Alexander von Humboldt-Stiftung.
Article copyright: © Copyright 1996 American Mathematical Society