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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Mean growth of Bloch functions and Makarov's law of the iterated logarithm


Authors: Rodrigo Bañuelos and Charles N. Moore
Journal: Proc. Amer. Math. Soc. 112 (1991), 851-854
MSC: Primary 30C35; Secondary 46E15
MathSciNet review: 1057948
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Abstract: The authors construct an example of a Bloch function on the unit disc whose circular $ {L^2}$ means grow at the maximal possible rate but which has no lower bound in the law of the iterated logarithm for Bloch functions. This answers a question of Przytycki [4, p. 154] and Makarov [3, p. 42].


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DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1057948-1
PII: S 0002-9939(1991)1057948-1
Article copyright: © Copyright 1991 American Mathematical Society