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For 1<p< \infty, weight w \in A_p, and any L ^2 -bounded Calder\'on-Zygmundoperator T, we show that there is a constant C(T,P) so that we prove the sharpnorm dependence on T_#, the maximal truncations of T, in both weak and strongtype L^p(w) norms. Namely, for the weak type norm, T_# maps L^p(w) toweak-L^p(w) with norm at most \|w\|_{A_p}. And for the strong type norm, thenorm estimate is \|w\|_{A_p}^{\max(1, (p-1) ^{-1})}. These estimates are notimprovable in the power of \lVert w\rVert_{A_p}. Our argument follows theoutlines of the arguments of Lacey-Petermichl-Reguera (Math.\ Ann.\ 2010) andHyt\"onen-P\'erez-Treil-Volberg (arXiv, 2010) with new ingredients, including aweak-type estimate for certain duals of T_#, and sufficient conditions for twoweight inequalities in L ^{p} for T_#. Our proof does not rely uponextrapolation.

Weak And Strong Type Estimates for Maximal Truncations of Calder\'on-Zygmund Operators on $ A_p$ Weighted Spaces