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

 

An inequality for the integral means of a Hadamard product


Author: Miroslav Pavlović
Journal: Proc. Amer. Math. Soc. 103 (1988), 404-406
MSC: Primary 30A10; Secondary 30D55
MathSciNet review: 943056
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Abstract: Motivated by Colzani's paper [1] we prove that

$\displaystyle {M_q}(r,f * g) \leq {(1 - r)^{1 - 1/p}}\left\Vert f \right\Vert p\left\Vert g \right\Vert q,\quad \;0{\text{ < }}r{\text{ < }}1,$

where $ 0{\text{ < }}p{\text{ < }}1,p \leq q \leq \infty $ and $ f * g$ is the Hadamard product of $ f \in {H^p}$ and $ g \in {H^q}$.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0943056-4
PII: S 0002-9939(1988)0943056-4
Keywords: Integral means, Hadamard product
Article copyright: © Copyright 1988 American Mathematical Society