Some remarks on Davis inequality for biparameter filtrations
Probability
2025-09-30 v1
Abstract
The Davis inequality between norms of square function of a martingale and its maximal function is known for martingales indexed by linearly ordered filtrations and in some particular cases for double indexed one. We prove the inequality for arbitrary filtrations satisfying the (F4) condition of Cairoli and Walsh and propose a method to attack the other inequality. The former is done by means of a two-parameter analogue of Davis-Garsia decomposition.
Cite
@article{arxiv.2509.23351,
title = {Some remarks on Davis inequality for biparameter filtrations},
author = {Maciej Rzeszut},
journal= {arXiv preprint arXiv:2509.23351},
year = {2025}
}