Tohoku Mathematical Journal

Sharp $L^p$-bounds for the martingale maximal function

Adam Osȩkowski

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Abstract

The paper studies sharp weighted $L^p$ inequalities for the martingale maximal function. Proofs exploit properties of certain special functions of four variables and self-improving properties of $A_p$ weights.

Article information

Source
Tohoku Math. J. (2), Volume 70, Number 1 (2018), 121-138.

Dates
First available in Project Euclid: 9 March 2018

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1520564421

Digital Object Identifier
doi:10.2748/tmj/1520564421

Mathematical Reviews number (MathSciNet)
MR3772808

Zentralblatt MATH identifier
06873676

Subjects
Primary: 60G44: Martingales with continuous parameter
Secondary: 60G42: Martingales with discrete parameter 42B25: Maximal functions, Littlewood-Paley theory

Keywords
martingale maximal function weighted inequality best constant

Citation

Osȩkowski, Adam. Sharp $L^p$-bounds for the martingale maximal function. Tohoku Math. J. (2) 70 (2018), no. 1, 121--138. doi:10.2748/tmj/1520564421. https://projecteuclid.org/euclid.tmj/1520564421


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