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Original Articles

Integral smoothness properties of some harmonic mappings

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Pages 95-110 | Received 28 Apr 1988, Published online: 26 Jun 2007
 

Abstract

Let be a univalent mapping of the unit disk (suitably normalized) onto a strip. We prove that the analytic completion of u, is the Cauihy trdnsiorm of a mcasure on the unii circle. It is also proven that if the range of such an f is starlike then the functions

are are convex in the direction of the imaginary axis for every φ.

AMS No:

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