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.
Citation
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
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