On Φ-inequalities for martingale fractional integration and their Bellman functions

2021/07/20 by Dmitriy Stolyarov, Stolyarov, Dmitriy
Mathematics · #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2107.09336

openalex publication_date 2021/07/20 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

Inspired by a conjecture of Vladimir Maz'ya on Φ-inequalities in the spirit of Bourgain and Brezis, we establish some Φ-inequalities for fractional martingale transforms. These inequalities may be thought of as martingale models of Φ-inequalities for differential operators. The proofs rest on new simple Bellman functions.

Related

• Fractional integration for irregular martingales
• Deviation probability bounds for fractional martingales and related remarks
• Probabilistic Approach to Fractional Integrals and the Hardy-Littlewood-Sobolev Inequality
• Martingale transforms and the Hardy-Littlewood-Sobolev inequality for semigroups
• Lecture notes on martingale inequalities