The A₂ theorem: Remarks and complements

2012/12/16 by Tuomas Hytönen, Hytönen, Tuomas P. · 2 citations
Mathematics · #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1212.3840

openalex publication_date 2012/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

I give a mini-survey of several approaches to the A₂ 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_∞ testing conditions, and the two-weight T1 theorem for positive dyadic operators).

Citations

• Two Weight Inequalities for Discrete Positive Operators
• Heating of the Ahlfors-Beurling operator: weakly quasiregular maps on the plane are quasiregular

Cited by

• Medians, Oscillations, and Distance Functions
• Matrix Weighted L^p Estimates in the Nonhomogeneous Setting

Related

• A simple proof of the A₂ conjecture
• Sharp weighted estimates for dyadic shifts and the A₂ conjecture
• Sharp A₂ estimates of Haar shifts via Bellman function
• Dyadic harmonic analysis and weighted inequalities: the sparse revolution
• A remark on two weight estimates for positive dyadic operators