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Proceedings of the American Mathematical Society

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

 

 

On a theorem of Hardy and Littlewood on the polydisc


Author: Hong Oh Kim
Journal: Proc. Amer. Math. Soc. 97 (1986), 403-409
MSC: Primary 32A35; Secondary 30D55
DOI: https://doi.org/10.1090/S0002-9939-1986-0840619-X
MathSciNet review: 840619
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Abstract: We prove the polydisc version of the theorem of Hardy and Littlewood on the fractional integral: If $ 0 < \alpha < 1/p$ and if $ f \in {H^p}$, then $ {I^\alpha }f \in {H^q}$ with $ q = p/(1 - \alpha p)$ where $ {I^\alpha }f$ is the fractional integral of $ f$ of order $ \alpha $.


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DOI: https://doi.org/10.1090/S0002-9939-1986-0840619-X
Keywords: Fractional integral, maximal theorem, Hardy space
Article copyright: © Copyright 1986 American Mathematical Society