Geodesic
A survey on the integral means spectrum for conformal mappings
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 157 (2015) no. 2, pp. 104-115

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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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     author = {I. R. Kayumov},
     title = {A survey on the integral means spectrum for conformal mappings},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {104--115},
     publisher = {mathdoc},
     volume = {157},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2015_157_2_a8/}
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I. R. Kayumov. A survey on the integral means spectrum for conformal mappings. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 157 (2015) no. 2, pp. 104-115. http://geodesic.mathdoc.fr/item/UZKU_2015_157_2_a8/