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

Abstract: 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 $1<p\le 2$.
 Subjects: Classical Analysis and ODEs (math.CA) Cite as: arXiv:1803.06981 [math.CA] (or arXiv:1803.06981v1 [math.CA] for this version)

## Submission history

From: Andrei Lerner [view email]
[v1] Mon, 19 Mar 2018 15:15:58 GMT (11kb)