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On the Analytic Part of Univalent Harmonic Mappings
Date Issued
01-06-2018
Author(s)
Abstract
In this article we obtain two sharp results concerning the analytic part of harmonic mappings f= h+ g¯ from the class SH0(S) which was recently introduced by Ponnusamy and Sairam Kaliraj. For example, we get the sharp estimate for | arg h′(z) | in the case when |z|≤1/2 and obtain the sharp radius of convexity for h. Our approach is applicable to a more general situation. Finally, we determine simple condition on the analytic part of univalent harmonic mappings so that it is in Hp spaces for 0 < p< 1 / 3.
Volume
12