A Bellman function proof of the L² bump conjecture

2012/02/11 by Fëdor Nazarov, Nazarov, Fedor, Alexander Reznikov +5
Mathematics · #42B20 #42B25 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #F.2.2 #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1202.2406

openalex publication_date 2012/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

We approach the problem of finding the sharp sufficient condition of the boundedness of all two weight Calderon--Zygmund operators. We solve this problem in L² by writing a formula for a Bellman function of the problem.

Citations

• Sharp A₂ estimates of Haar shifts via Bellman function
• Sharp weighted estimates for dyadic shifts and the A₂ conjecture

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• Logarithmic bump conditions and the two weight boundedness of Calderón-Zygmund operators
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• The Linear Bound in A₂ for Calderón-Zygmund Operators: A Survey