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Summer 2008 On some weighted norm inequalities for Littlewood–Paley operators
Andrei K. Lerner
Illinois J. Math. 52(2): 653-666 (Summer 2008). DOI: 10.1215/ijm/1248355356

Abstract

It is shown that the $L^p_w,1<p<\infty$, operator norms of Littlewood--Paley operators are bounded by a multiple of $\|w\|_{A_p}^{\gamma_p}$, where $\gamma_p=\max\{1,p/2\}\frac {1}{p-1}$. This improves previously known bounds for all $p>2$. As a corollary, a new estimate in terms of $\|w\|_{A_p}$ is obtained for the class of Calderón-Zygmund singular integrals commuting with dilations.

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Andrei K. Lerner. "On some weighted norm inequalities for Littlewood–Paley operators." Illinois J. Math. 52 (2) 653 - 666, Summer 2008. https://doi.org/10.1215/ijm/1248355356

Information

Published: Summer 2008
First available in Project Euclid: 23 July 2009

zbMATH: 1177.42016
MathSciNet: MR2524658
Digital Object Identifier: 10.1215/ijm/1248355356

Subjects:
Primary: 42B20, 42B25

Rights: Copyright © 2008 University of Illinois at Urbana-Champaign

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Vol.52 • No. 2 • Summer 2008
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