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On some weighted norm inequalities for Littlewood–Paley operators

2008; Duke University Press; Volume: 52; Issue: 2 Linguagem: Inglês

10.1215/ijm/1248355356

1945-6581

Andrei K. Lerner,

Nonlinear Partial Differential Equations

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.