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 (4)

• Non-probabilistic proof of the A_2 theorem, and sharp weighted bounds for the q-variation of singular integrals
• Two Weight Inequality for the Hilbert Transform: A Real Variable Characterization, I
• Two Weight Inequalities for Discrete Positive Operators
• On $A_2$ conjecture and corona decomposition of weights

Cited by in corpus (11)

• On weighted norm inequalities for the Carleson and Walsh-Carleson operators
• Sparse domination of sharp variational truncations
• Two weight norm inequalities for fractional integral operators and commutators
• $A_p$-$A_{\infty }$ estimates for multilinear maximal and sparse operators
• A new two weight estimates for a vector-valued positive operator
• Another proof of Scurry's characterization of a two weight norm inequality for a sequence-valued positive dyadic operator
• The trilinear embedding theorem
• Two weight $L^p$ estimates for paraproducts in non-homogeneous settings
• A characterization of two weight trace inequalities for positive dyadic operators in the upper triangle case
• Fractional operators on weighted Morrey spaces
• The $n$ linear embedding theorem