The A_2 theorem: Remarks and complements

Abstract

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 $A_p$--$A_{\infty }$ testing conditions, and the two-weight $T1$ theorem for positive dyadic operators).

15 pages, 1 figure; submitted to proceedings of El Escorial 2012

References in corpus (1)

• On $A_2$ conjecture and corona decomposition of weights

Cited by in corpus (2)

• Another proof of Scurry's characterization of a two weight norm inequality for a sequence-valued positive dyadic operator
• A characterization of two weight trace inequalities for positive dyadic operators in the upper triangle case