Geodesic
The integral means spectrum and the law of the iterated logarithm for conformal mappings
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 148 (2006) no. 2, pp. 85-96

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The present survey paper is described most important results about estimates of the integral means for derivatives of conformal maps of the unit disk into simply connected domains on the complex plane. Detailed description of the results connected with estimates of the integral means spectrum near the origin and also near the point $t=-2$ is given. Results connected with Makarov's law of the iterated logarithm are described. A connection between the integral means spectrum and the law of iterated logarithm is shown. On this basis metrical properties of harmonic measure on Jordan curves are improved. 
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     author = {I. R. Kayumov},
     title = {The integral means spectrum and the law of the iterated logarithm for conformal mappings},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {85--96},
     publisher = {mathdoc},
     volume = {148},
     number = {2},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2006_148_2_a8/}
}
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I. R. Kayumov. The integral means spectrum and the law of the iterated logarithm for conformal mappings. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 148 (2006) no. 2, pp. 85-96. http://geodesic.mathdoc.fr/item/UZKU_2006_148_2_a8/