Open Access
2022 Weak-type estimates for martingale maximal functions
Adam Osękowski, Mateusz Wojtas
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Electron. Commun. Probab. 27: 1-11 (2022). DOI: 10.1214/22-ECP494


The paper contains the study of sharp extensions of weak-type estimates for a martingale maximal function. Given 1<p< and a pair (x,y) of nonnegative numbers satisfying xpy, we identify the optimal upper bounds for |supnfn|p,, for nonnegative martingales f=(fn)n0 satisfying f1=x and fpp=y.


The authors would like to express their gratitude to the anonymous Referees for the careful reading of the first version of the paper, many helpful comments and suggestions.


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Adam Osękowski. Mateusz Wojtas. "Weak-type estimates for martingale maximal functions." Electron. Commun. Probab. 27 1 - 11, 2022.


Received: 11 June 2022; Accepted: 16 October 2022; Published: 2022
First available in Project Euclid: 23 October 2022

MathSciNet: MR4368695
Digital Object Identifier: 10.1214/22-ECP494

Primary: 60G42 , 60G44

Keywords: best constants , Burkholder’s method , maximal , weak-type

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