Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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}$.


References [Enhancements On Off] (What's this?)

  • [1] Patrick Billingsley, Ergodic theory and information, John Wiley & Sons, Inc., New York-London-Sydney, 1965. MR 0192027
  • [2] J. Clunie and Ch. Pommerenke, On the coefficients of univalent functions, Michigan Math. J. 14 (1967), 71–78. MR 0207974
  • [3] Peter L. Duren, Univalent functions, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 259, Springer-Verlag, New York, 1983. MR 708494
  • [4] J. Feng and T. MacGregor, Estimates on integral means of the derivative of univalent functions, J. Analyse Math. 29 (1976), 203-231.
  • [5] John Hawkes, Probabilistic behaviour of some lacunary series, Z. Wahrsch. Verw. Gebiete 53 (1980), no. 1, 21–33. MR 576895, 10.1007/BF00531609
  • [6] Problems in complex function theory, Bull. London Math. Soc. 4 (1972), 354–366. MR 0480954
  • [7] Christian Pommerenke, Univalent functions, Vandenhoeck & Ruprecht, Göttingen, 1975. With a chapter on quadratic differentials by Gerd Jensen; Studia Mathematica/Mathematische Lehrbücher, Band XXV. MR 0507768
  • [8] -, On the integral means of the derivative of a univalent function, J. London Math. Soc. (to appear).

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30C55, 30B10

Retrieve articles in all journals with MSC: 30C55, 30B10


Additional Information

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