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May 2009 Paley's inequality of integral transform type
Yuichi KANJIN, Kunio SATO
Hokkaido Math. J. 38(2): 233-247 (May 2009). DOI: 10.14492/hokmj/1248190076

Abstract

Let $\{n_k\}_{k=1}^\infty$ be a sequence of positive integers with Hadamard gap. For an analytic function $F(z) = \sum_{n=0}^{\infty}a_n z^n$ in the unit disc satisfying $\sup_{0 \lt r \lt 1}$ $\int_0^{2\pi} |F(re^{i\theta})|\, d\theta \lt \infty$, the inequality $( \sum_{k=1}^{\infty}|a_{n_k}|^2 )^{1/2} \lt \infty$ holds, which is familiar as Paley's inequality. In this paper, an integral transform version of this inequality is established.

Citation

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Yuichi KANJIN. Kunio SATO. "Paley's inequality of integral transform type." Hokkaido Math. J. 38 (2) 233 - 247, May 2009. https://doi.org/10.14492/hokmj/1248190076

Information

Published: May 2009
First available in Project Euclid: 21 July 2009

zbMATH: 1179.42006
MathSciNet: MR2522913
Digital Object Identifier: 10.14492/hokmj/1248190076

Subjects:
Primary: 42A38
Secondary: 42A55

Rights: Copyright © 2009 Hokkaido University, Department of Mathematics

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Vol.38 • No. 2 • May 2009
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