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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2509.23351 |
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| _version_ | 1866908562789236736 |
|---|---|
| author | Rzeszut, Maciej |
| author_facet | Rzeszut, Maciej |
| contents | The Davis inequality $\mathbb{E} Sf\simeq \mathbb{E} f^*$ between $L^1$ 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 $\gtrsim $ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_23351 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some remarks on Davis inequality for biparameter filtrations Rzeszut, Maciej Probability The Davis inequality $\mathbb{E} Sf\simeq \mathbb{E} f^*$ between $L^1$ 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 $\gtrsim $ 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. |
| title | Some remarks on Davis inequality for biparameter filtrations |
| topic | Probability |
| url | https://arxiv.org/abs/2509.23351 |