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Quantitative weighted estimates are obtained for the Littlewood-Paley squarefunction $S$ associated with a lacunary decomposition of ${\mathbb R}$ and forthe Marcinkiewicz multiplier operator. In particular, we find the sharpdependence on $[w]_{A_p}$ for the $L^p(w)$ operator norm of $S$ for $1<p\le 2$.

Quantitative weighted estimates for the Littlewood-Paley square function and Marcinkiewicz multipliers