Illinois Journal of Mathematics

On some weighted norm inequalities for Littlewood–Paley operators

Andrei K. Lerner

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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.

Article information

Source
Illinois J. Math., Volume 52, Number 2 (2008), 653-666.

Dates
First available in Project Euclid: 23 July 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1248355356

Digital Object Identifier
doi:10.1215/ijm/1248355356

Mathematical Reviews number (MathSciNet)
MR2524658

Zentralblatt MATH identifier
1177.42016

Subjects
Primary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42B25: Maximal functions, Littlewood-Paley theory

Citation

Lerner, Andrei K. On some weighted norm inequalities for Littlewood–Paley operators. Illinois J. Math. 52 (2008), no. 2, 653--666. doi:10.1215/ijm/1248355356. https://projecteuclid.org/euclid.ijm/1248355356


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