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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The Hardy class of a function with slowly-growing area


Author: Lowell J. Hansen
Journal: Proc. Amer. Math. Soc. 45 (1974), 409-410
MSC: Primary 30A78
DOI: https://doi.org/10.1090/S0002-9939-1974-0350006-0
MathSciNet review: 0350006
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Abstract: In this paper we show that if $ f$ is analytic on the open unit disk and if the area of $ [\{ \vert z\vert \leq R\} \cap {\text{image of }}f]$ grows sufficiently slowly as a function of $ R$, then $ f$ belongs to the Hardy class $ {H^p}$ for all $ p$ satisfying $ 0 < p < + \infty $.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0350006-0
Keywords: Hardy classes, functions with finite area
Article copyright: © Copyright 1974 American Mathematical Society