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Positive harmonic majorization of the real part of a holomorphic function


Author: Stephen J. Gardiner
Journal: Proc. Amer. Math. Soc. 117 (1993), 767-770
MSC: Primary 30D35
DOI: https://doi.org/10.1090/S0002-9939-1993-1139468-0
MathSciNet review: 1139468
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Abstract: Let $ U$ be the unit disc. This paper investigates which domains $ D$ in the complex plane have the property that $ \mathcal{R}ef$ belongs to $ {h^1}$, or the more restrictive property that $ {e^f}$ belongs to the Smirnov class $ {\mathcal{N}^ + }$, for every holomorphic function $ f:U \to D$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1139468-0
Article copyright: © Copyright 1993 American Mathematical Society

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