The A_2 theorem: Remarks and complements

I give a mini-survey of several approaches to the $A_2$ theorem, biased towards the “corona” rather than the “Bellman” side of the coin. There are two new results (a streamlined form of Lerner’s local oscillation formula, and the sharpness of the linear-in-complexity weak $(1,1)$ bound for dyadic shifts) and two new proofs of known results (the $A_p$–$A_{\mathrm{\infty }}$ testing conditions, and the two-weight $T1$ theorem for positive dyadic operators).