A simple proof of the $A_2$ conjecture

By Andrei K. Lerner. 2012

145 citations recorded by the source corpus.

We give a simple proof of the $A_2$ conjecture proved recently by T. Hyt\"onen. Our proof avoids completely the notion of the Haar shift operator, and it is based only on the "local mean oscillation decomposition". Also our proof yields a simple proof of the "two-weight conjecture" as well.

View Paper: https://www.semanticscholar.org/paper/08da225ae8a388c782fb41a6d77936bce04011ea

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Citations in the corpus

• Sparse bilinear forms for Bochner Riesz multipliers and applications (2016, unknown): “Firstly, Lerner [24, 25] proved that the norm of a C-Z operator in a Banach function space is dominated by sparse positive operators.”
• The Sharp Weighted Bound for Multilinear Maximal Functions and Calderón–Zygmund Operators (2012, background): “Later is was proven by Hyt¨onen [8] that if T is a Calder´on-Zygmund operator then (1.2) Again, we refer the reader to [9, 12] for the background material and further references.”
• Sharp weighted norm estimates beyond Calderón–Zygmund theory (2015, unknown): “…this extra property, we are going to detail an “elementary” proof of the sharp weighted estimates (simpler than all the existing proofs, such as [Lerner 2013b; Lacey 2015]), which has also the very important property that is extends to nonintegral operators with no regularity property on the…”