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

 

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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0818450-0
PII: S 0002-9939(1986)0818450-0
Keywords: Univalent functions, integral means of the derivative, lacunary series, ergodic theorem, Hausdorff measures
Article copyright: © Copyright 1986 American Mathematical Society