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

Quantitative weighted estimates are obtained for the Littlewood–Paley square function $S$ associated with a lacunary decomposition of $\mathbb{R}$ and for the Marcinkiewicz multiplier operator. In particular, we find the sharp dependence on $[w]_{A_p}$ for the $L^p (w)$ operator norm of $S$ for $1 \lt p \leq 2$.

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The author was supported by ISF grant No. 447/16 and ERC Starting Grant No. 713927.

Received 30 March 2018

Accepted 8 November 2018

Published 12 August 2019