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arXiv · 1803.06981

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

Andrei K. Lerner
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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 $1<p\le 2$.

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Andrei K. Lerner. 2018-03-19. Quantitative weighted estimates for the Littlewood-Paley square function and Marcinkiewicz multipliers. https://arxiv.org/abs/1803.06981

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