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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}$.

References [Enhancements On Off] (What's this?)

  • [1] Leonardo Colzani, Cesàro means of power series, Boll. Un. Mat. Ital. A (6) 3 (1984), no. 1, 147–149 (English, with Italian summary). MR 739202
  • [2] Peter L. Duren, Theory of 𝐻^{𝑝} spaces, Pure and Applied Mathematics, Vol. 38, Academic Press, New York-London, 1970. MR 0268655

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Keywords: Integral means, Hadamard product
Article copyright: © Copyright 1988 American Mathematical Society

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