A characterization of Hardy-Orlicz spaces on planar domains
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- by Manfred Stoll
- Proc. Amer. Math. Soc. 117 (1993), 1031-1038
- DOI: https://doi.org/10.1090/S0002-9939-1993-1124151-8
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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 \[ \iint _D {\delta (z)\phi ''(\log |f(z)|)\frac {{|f’(z){|^2}}} {{|f(z){|^2}}}dx dy < \infty ,}\] 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 $t$.References
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Bibliographic Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 117 (1993), 1031-1038
- MSC: Primary 46E10; Secondary 30D55, 46J15
- DOI: https://doi.org/10.1090/S0002-9939-1993-1124151-8
- MathSciNet review: 1124151