The Ap-Ainfty inequality for general Calderon-Zygmund operators Tuomas HytonenMichael Lacey 42B2542B35Calderon-Zygmund Operatorsweights 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 $w\in A_p$: \[ \|T_{\natural}f\|_{L^p(w)}\leq C_{T,p}\big[w\big]_{A_p}^{1/p}\big(\big[w\big]_{A_{\infty}}^{1/p'}+\big[w^{1-p'}\big]_{A_{\infty}}^{1/p}\big)\|f\|_{L^p(w)}. \] Indiana University Mathematics Journal 2012 text pdf 10.1512/iumj.2012.61.4777 10.1512/iumj.2012.61.4777 en Indiana Univ. Math. J. 61 (2012) 2041 - 2052 state-of-the-art mathematics http://iumj.org/access/