Extremizers and Bellman function for martingale weak type inequality

2013/11/09 by Alexander Reznikov, Reznikov, Alexander, Vasiliy Vasyunin +3 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Approximation and Integration #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1311.2133

openalex publication_date 2013/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an exact formula for the Bellman function of the weak type of martingale transform. We also give the extremal functions (actually extremal sequences of functions). We find them using the precise form of the Bellman function. The extremal examples have a fractal nature as it often happens in that kind of problems. This article is devoted to the unweighted weak type estimate.

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

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