On weak weighted estimates of the martingale transform and a dyadic shift (Q1639706)

This article is based on following preprints of the authors [``A Bellman function counterexample to the \(A_1\) conjecture: the blow-up of the weak norm estimates of weighted singular operators'', Preprint, \url{arXiv:1506.04710}] and [``On weak weighted estimates of martingale transform'', Preprint, \url{arXiv:1612.03958}]. The authors consider several weak type estimates for singular operators using the Bellman function approach. They disprove the \(A_1\) conjecture, which is weaker than Muckenhoupt-Wheeden conjecture disproved by \textit{M. C. Reguera} [Adv. Math. 227, No. 4, 1436--1450 (2011; Zbl 1221.42026)] and \textit{M. C. Reguera} and \textit{C. Thiele} [Math. Res. Lett. 19, No. 1, 1--7 (2012; Zbl 1271.42025)].