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We obtain an $L^p(w)$ bound for Calder\'on-Zygmund operators $T$ when $w\in A_1$. This bound is sharp both with respect to $\|w\|_{A_1}$ and with respect to $p$. As a result, we get a new $L^{1,\infty}(w)$ estimate for $T$ related to a problem of Muckenhoupt and Wheeden.

$A_1$ bounds for Calderón-Zygmund operators related to a problem of Muckenhoupt and Wheeden