Positive harmonic majorization of the real part of a holomorphic function

Gardiner, Stephen J.

doi:10.1090/S0002-9939-1993-1139468-0

Positive harmonic majorization of the real part of a holomorphic function
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Proc. Amer. Math. Soc. 117 (1993), 767-770 Request permission

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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Potentials d’équilibre et capacité des ensembles avec quelques applications à la théorie des fonctions

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