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Estimates for Integral Means of Hyperbolically Convex Functions

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Abstract

We prove the Mejia-Pommerenke conjecture that the Taylor coefficients of hyperbolically convex functions in the disk behave like O(log−2(n)/n) as n → ∞ assuming that the image of the unit disk under such functions is a domain of bounded boundary rotation. Moreover, we obtain some asymptotically sharp estimates for the integral means of the derivatives of such functions and consider an example of a hyperbolically convex function that maps the unit disk onto a domain of infinite boundary rotation.

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Authors and Affiliations

  1. N. Chebotarev Research Institute of Mathematics and Mechanics, Kazan', Russia

    I. R. Kayumov & Yu. V. Obnosov

Authors
  1. I. R. Kayumov
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  2. Yu. V. Obnosov
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Additional information

Original Russian Text Copyright © 2005 Kayumov I. R. and Obnosov Yu. V.

The authors were partially supported by the Russian Foundation for Basic Research (Grants 05-01-00523, 03-01-00015, and 03-01-96193-p2003Tatarstan-a).

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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 6, pp. 1316–1323, November–December, 2005.

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Kayumov, I.R., Obnosov, Y.V. Estimates for Integral Means of Hyperbolically Convex Functions. Sib Math J 46, 1062–1068 (2005). https://doi.org/10.1007/s11202-005-0100-4

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  • DOI: https://doi.org/10.1007/s11202-005-0100-4

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