2023 On Maz’ya’s Φ-Inequalities for Martingale Fractional Integration and Their Bellman Functions
Dmitriy Stolyarov
Michigan Math. J. Advance Publication 1-18 (2023). DOI: 10.1307/mmj/20216116

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.

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Dmitriy Stolyarov. "On Maz’ya’s Φ-Inequalities for Martingale Fractional Integration and Their Bellman Functions." Michigan Math. J. Advance Publication 1 - 18, 2023. https://doi.org/10.1307/mmj/20216116

Information

Received: 28 July 2021; Revised: 30 November 2021; Published: 2023
First available in Project Euclid: 30 May 2023

Digital Object Identifier: 10.1307/mmj/20216116

Keywords: 60G42 , 60G46

Rights: Copyright © 2023 The University of Michigan

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