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Radial Divergence in BMOA
Author(s) -
Ullrich David C.
Publication year - 1994
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-68.1.145
Subject(s) - mathematics , holomorphic function , bloch space , mathematical analysis , hardy space , divergence (linguistics) , unit sphere , ball (mathematics) , space (punctuation) , boundary (topology) , pure mathematics , compact space , philosophy , linguistics
The set of boundary points at which a BMOA function in the unit ball of C d fails to have a radial limit may be an arbitrary G δ of measure zero. Similar results are given for the Bloch space and for VMOA. As an application it is shown that there exist functions with no radial limits in the holomorphic Besov spaces interpolating between the Hardy space H 2 and the Bloch space.