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Fall 2000 On a singular integral estimate for the maximum modulus of a canonical product
Faruk F. Abi-Khuzam, Bassam Shayya
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Illinois J. Math. 44(3): 551-555 (Fall 2000). DOI: 10.1215/ijm/1256060415

Abstract

If $f$ is a canonical product with only real negative zeros and non-integral order $\rho,n(t,0)$ is the zero counting function, and $B(r,f)=\mathrm{sup}_{0 \lt \theta \lt \pi}|\log f(re^{i \theta})|$, then $$r^{-q-1}B(r,f) \leq \pi\{M \varphi(r) + MH\varphi(r)\}+\int_{0}^{\infty}{\frac{\varphi(t)dt}{t+r}},$$ where $\varphi(t) = t^{-q-1} n(t,0)$, $H$ is the Hilbert transform operator and $M$ is the Hardy-Littlewood maximal operator.

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Faruk F. Abi-Khuzam. Bassam Shayya. "On a singular integral estimate for the maximum modulus of a canonical product." Illinois J. Math. 44 (3) 551 - 555, Fall 2000. https://doi.org/10.1215/ijm/1256060415

Information

Published: Fall 2000
First available in Project Euclid: 20 October 2009

zbMATH: 0961.30021
MathSciNet: MR1772428
Digital Object Identifier: 10.1215/ijm/1256060415

Subjects:
Primary: 30D20
Secondary: 30D35 , 42A50

Rights: Copyright © 2000 University of Illinois at Urbana-Champaign

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Vol.44 • No. 3 • Fall 2000
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