A Distortion Theorem for Univalent Gap Series

Author： Kayumov I. R.  

Publisher： Springer Publishing Company

ISSN： 0037-4466

Source： Siberian Mathematical Journal, Vol.44, Iss.6, 2003-11, pp. : 997-1002

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Abstract

We prove a distortion theorem for conformal mappings of the unit disk for which log f′ is representable as the Hadamard gap series. This theorem implies in particular that such conformal mapping is “almost” bounded, i.e., for every ε>0, there is a positive constant Cε such that |f,(z)|≤Cε(1−|z|) −ε.

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