The paper contains the study of sharp extensions of weak-type estimates for a martingale maximal function. Given and a pair of nonnegative numbers satisfying , we identify the optimal upper bounds for , for nonnegative martingales satisfying and .
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.
"Weak-type estimates for martingale maximal functions." Electron. Commun. Probab. 27 1 - 11, 2022. https://doi.org/10.1214/22-ECP494