2025/09/27 by Maciej Rzeszut, Rzeszut, Maciej
Computer Science · Mathematics · #Advanced Banach Space Theory #FOS: Mathematics #Optimization and Variational Analysis #Point processes and geometric inequalities #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2509.23351
openalex publication_date 2025/09/27 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28
The Davis inequality 𝔼 Sf≃ 𝔼 f^* between L1 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.