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arXiv · 1509.00273

Weak and strong $A_p$-$A_\infty$ estimates for square functions and related operators

Tuomas P. Hytönen·Kangwei Li
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Abstract

We prove sharp weak and strong type weighted estimates for a class of dyadic operators that includes majorants of both standard singular integrals and square functions. Our main new result is the optimal bound $[w]_{A_p}^{1/p}[w]_{A_\infty}^{1/2-1/p}\lesssim [w]_{A_p}^{1/2}$ for the weak type norm of square functions on $L^p(w)$ for $p>2$; previously, such a bound was only known with a logarithmic correction. By the same approach, we also recover several related results in a streamlined manner.

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Tuomas P. Hytönen, Kangwei Li. 2017-07-27. Weak and strong $A_p$-$A_\infty$ estimates for square functions and related operators. https://arxiv.org/abs/1509.00273

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