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 Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki: Year: Volume: Issue: Page: Find

 Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2015, Volume 157, Book 2, Pages 104–115 (Mi uzku1310)

A survey on the integral means spectrum for conformal mappings

I. R. Kayumov

Kazan (Volga Region) Federal University, Kazan, Russia

Abstract: The present survey is devoted to the description of the results about estimates of the integral means in various classes of analytic functions. Great importance is given to the boundary properties of conformal mappings. The systematic results on the estimation of the integral means spectrum and the well-known law of the iterated logarithm for conformal mappings, which was proven by N. G. Makarov in 1985, were the basic mathematical tools for this study. Precise estimates of the integral means in various subclasses of univalent functions are described. Estimates of the integral means spectrum in the class of functions mapping the exterior of the unit disk onto the attraction basins of the infinity of algebraic polynomials are presented.

Keywords: conformal mappings, integral means spectrum, harmonic measure.

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UDC: 517.54

Citation: I. R. Kayumov, “A survey on the integral means spectrum for conformal mappings”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 157, no. 2, Kazan University, Kazan, 2015, 104–115

Citation in format AMSBIB
\Bibitem{Kay15} \by I.~R.~Kayumov \paper A survey on the integral means spectrum for conformal mappings \serial Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki \yr 2015 \vol 157 \issue 2 \pages 104--115 \publ Kazan University \publaddr Kazan \mathnet{http://mi.mathnet.ru/uzku1310} \elib{http://elibrary.ru/item.asp?id=23819781}