A Bellman function proof of the L² bump conjecture

2012/02/11 by Fedor Nazarov, Fëdor Nazarov, Alexander Reznikov +6 · 2 citations
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 #acm:42B20 #acm:42B25 #math.AP #math.CA #msc:42B20 #msc:42B25

paper · pdf · doi:10.48550/arxiv.1202.2406

23 pages, the third version

openalex publication_date 2012/02/11 · arxiv created 2014/04/08 · arxiv updated 2014/04/09 · 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

Cited by

• Carleson--Buckley measures beyond the scope of A_∞ and their applications
• Bellman approach to the one-sided bumping for weighted estimates of Calderón--Zygmund operators

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