A Bellman function counterexample to the A₁ conjecture: the blow-up of the weak norm estimates of weighted singular operators

2015/06/15 by Fëdor Nazarov, Nazarov, F., Alexander Reznikov +5 · 1 citation
Mathematics · #42B20 #42B37 #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #F.2.2 #FOS: Mathematics #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1506.04710

openalex publication_date 2015/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider several weak type estimates for singular operators using the Bellman function approach. We disprove the A₁ conjecture, thus strengthening the counterexamples built by Reguera--Thiele. We show a certain logarithmic blow-up for the end-point estimates of important weighted singular operators.

Citations

• Extremizers and Bellman function for martingale weak type inequality

Cited by

• A₁ theory of weights for rough homogeneous singular integrals and commutators

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