Abstract
We show that N.G. Makarov’s law of the iterated logarithm governs the radial growth of weighted Bloch functions in the complex unit ball. The argument is based on an analog of M. Weiss’ theorem for special lacunary series in the ball.
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References
A. B. Aleksandrov, Proper holomorphic mappings from the ball to the polydisk, Dokl. Akad. Nauk SSSR 286 (1986), 11–15 (Russian); English transl.: Soviet Math. Dokl. 33 (1986), 1–5.
R. Bañuelos and Ch. N. Moore, Probabilistic behavior of harmonic functions, Progress in Mathematics, vol. 175, Birkhäuser Verlag, Basel, 1999.
Doubtsov E.: Weighted Bloch spaces and quadratic integrals. J. Math. Anal. Appl. 412, 269–276 (2014)
Makarov N. G.: On the distortion of boundary sets under conformal mappings. Proc. London Math. Soc. 51, 369–384 (1985)
Ryll J., Wojtaszczyk P.: On homogeneous polynomials on a complex ball. Trans. Amer. Math. Soc. 276, 107–116 (1983)
Shields A.L., Williams D.L.: Bonded projections, duality, and multipliers in spaces of analytic functions. Trans. Amer. Math. Soc. 162, 287–302 (1971)
Ullrich D.C.: A Bloch function in the ball with no radial limits. Bull. London Math. Soc. 20, 337–341 (1988)
Weiss M.: The law of the iterated logarithm for lacunary trigonometric series. Trans. Amer. Math. Soc. 91, 444–469 (1959)
Yang C., Xu W.: Spaces with normal weights and Hadamard gap series. Arch. Math. (Basel) 96, 151–160 (2011)
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The author was supported by the Russian Science Foundation (Grant No. 14-11-00012).
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Doubtsov, E. Radial growth of Bloch functions in the complex ball. Arch. Math. 102, 391–399 (2014). https://doi.org/10.1007/s00013-014-0637-1
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DOI: https://doi.org/10.1007/s00013-014-0637-1