Fractional integration for irregular martingales

2020/09/11 by Dmitriy Stolyarov, Stolyarov, Dmitriy, Dmitry Yarcev +1
Computer Science · Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2009.05293

openalex publication_date 2020/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We suggest two versions of the Hardy--Littlewood--Sobolev inequality for discrete time martingales. In one version, the fractional integration operator is a martingale transform, however, it may vanish if the filtration is excessively irregular; the second version lacks the martingale property while being analytically meaningful for an arbitrary filtration.

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