ON FUNCTIONS IN THE LITTLE BLOCH SPACE AND INNER FUNCTIONS

Authors
ROHDE S
Citation
S. Rohde, ON FUNCTIONS IN THE LITTLE BLOCH SPACE AND INNER FUNCTIONS, Transactions of the American Mathematical Society, 348(7), 1996, pp. 2519-2531
Citations number
18
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Transactions of the American Mathematical Society → ACNP
ISSN journal
00029947
Volume
348
Issue
7
Year of publication
1996
Pages
2519 - 2531
Database
ISI
SICI code
0002-9947(1996)348:7<2519:OFITLB>2.0.ZU;2-6
Abstract
We prove that analytic functions in the little Bloch space assume ever y 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 charact erizations of various classes of Bloch functions in terms of their lev el sets are given.