On functions in the little Bloch space and inner functions

Rohde, S.

doi:10.1090/S0002-9947-96-01497-3

On functions in the little Bloch space and inner functions
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by S. Rohde

Trans. Amer. Math. Soc. 348 (1996), 2519-2531

DOI: https://doi.org/10.1090/S0002-9947-96-01497-3

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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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