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A note on integral means of the derivative in conformal mapping

Author: N. G. Makarov
Journal: Proc. Amer. Math. Soc. 96 (1986), 233-235
MSC: Primary 30C55; Secondary 30B10
MathSciNet review: 818450
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Abstract: There exists a number $ {p_0} > 1/3$ such that among the derivatives of univalent functions, that of the Koebe function ceases to have the greatest order of growth of $ {L^p}$-means for all $ p \leq {p_0}$.

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Keywords: Univalent functions, integral means of the derivative, lacunary series, ergodic theorem, Hausdorff measures
Article copyright: © Copyright 1986 American Mathematical Society

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