A note on a two-weight estimate for the dyadic square function

A note on a two-weight estimate for the dyadic square function
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by Spyridon Kakaroumpas PDF

Proc. Amer. Math. Soc. 147 (2019), 3377-3388 Request permission

We show that the two-weight estimate for the dyadic square function proved by Lacey–Li is sharp.

References

Tuomas P. Hytönen and Michael T. Lacey, The $A_p$-$A_\infty$ inequality for general Calderón-Zygmund operators, Indiana Univ. Math. J. 61 (2012), no. 6, 2041–2092. MR 3129101, DOI 10.1512/iumj.2012.61.4777
Tuomas P. Hytönen and Kangwei Li, Weak and strong $A_p$-$A_\infty$ estimates for square functions and related operators, Proc. Amer. Math. Soc. 146 (2018), no. 6, 2497–2507. MR 3778152, DOI 10.1090/proc/13908
Michael T. Lacey, An elementary proof of the $A_2$ bound, Israel J. Math. 217 (2017), no. 1, 181–195. MR 3625108, DOI 10.1007/s11856-017-1442-x
Michael T. Lacey and Kangwei Li, On $A_p$–$A_\infty$ type estimates for square functions, Math. Z. 284 (2016), no. 3-4, 1211–1222. MR 3563275, DOI 10.1007/s00209-016-1696-8
M. T. Lacey and J. Scurry, Weighted weak type estimates for square functions, preprint, arXiv:1211.4219v1 [math.CA], 2012.
Jingguo Lai and Sergei Treil, Two weight $L^p$ estimates for paraproducts in non-homogeneous settings, J. Funct. Anal. 275 (2018), no. 1, 45–72. MR 3799623, DOI 10.1016/j.jfa.2017.11.008
Andrei K. Lerner, On some sharp weighted norm inequalities, J. Funct. Anal. 232 (2006), no. 2, 477–494. MR 2200743, DOI 10.1016/j.jfa.2005.08.006
Fedor Nazarov, Stefanie Petermichl, Sergei Treil, and Alexander Volberg, Convex body domination and weighted estimates with matrix weights, Adv. Math. 318 (2017), 279–306. MR 3689742, DOI 10.1016/j.aim.2017.08.001