article

Title: The Ap-Ainfty inequality for general Calderon-Zygmund operators

Authors: Tuomas P Hytonen and Michael Lacey

Issue: Volume 61 (2012), Issue 6, 2041-2052

Abstract:

$Let $T$ be an arbitrary $L^2$-bounded Calder\'on-Zygmund operator, and $T_{\natural}$ its maximal truncated version. This, then, satisfies the following bound for all $p\in(1,\infty)$ and all $w\in A_p$: \[ \|T_{\natural}f\|_{L^p(w)}\leq C_{T,p}\big[w\big]_{A_p}^{1/p}\big(\big[w\big]_{A_{\infty}}^{1/p'}+\big[w^{1-p'}\big]_{A_{\infty}}^{1/p}\big)\|f\|_{L^p(w)}. \]$