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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
DOI: https://doi.org/10.1090/S0002-9939-1991-1057948-1
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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  • [1] P. Erdös and I. S. Gál, On the law of the iterated logarithm, Nederl. Akad. Wetensch. Proc. Ser. A 58 (1955), 65-84.
  • [2] N. G. Makarov, On the distortion of boundary sets under conformal mappings, Proc. London Math. Soc. 51 (1985), 369-384. MR 794117 (87d:30012)
  • [3] -, Probability methods in conformal mappings I, II, LOMI preprints, USSR Acad. Sci. Steklov Math. Inst. Leningrad, 1988.
  • [4] F. Przytycki, On the law of the iterated logarithm for Bloch functions, Studia Math. 93 (1989), 145-154. MR 1002917 (91f:30044)
  • [5] R. Salem and A. Zygmund, La loi du logarithme itéré pour les séries trigonométriques lacunaires, Bull. Sci. Math. 74 (1950), 209-224. MR 0039828 (12:605c)
  • [6] D. Ullrich, personal communication.
  • [7] M. Weiss, The law of the iterated logarithm for lacunary trigonometric series, Trans. Amer. Math. Soc. 91 (1959), 444-469. MR 0108681 (21:7396)

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DOI: https://doi.org/10.1090/S0002-9939-1991-1057948-1
Article copyright: © Copyright 1991 American Mathematical Society

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