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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

A characterization of Hardy-Orlicz spaces on planar domains


Author: Manfred Stoll
Journal: Proc. Amer. Math. Soc. 117 (1993), 1031-1038
MSC: Primary 46E10; Secondary 30D55, 46J15
MathSciNet review: 1124151
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Abstract: In the paper we prove that for a wide class of bounded domains $ D$ in $ \mathbb{C}$, a holomorphic function $ f$ is in the Hardy-Orlicz space $ {H_\phi }(D)$ if and only if

$\displaystyle \iint_D {\delta (z)\phi ''(\log \vert f(z)\vert)\frac{{\vert f'(z){\vert^2}}} {{\vert f(z){\vert^2}}}dx\,dy < \infty ,}$

where $ \delta (z)$ denotes the distance from $ z$ to the boundary of $ D$ and $ \phi $ is a strongly convex function on $ ( - \infty ,\infty )$ for which $ \phi ''(t)$ exists for all $ t$.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1124151-8
PII: S 0002-9939(1993)1124151-8
Article copyright: © Copyright 1993 American Mathematical Society