可预测从属、尖锐鞅不等式及其应用
Predictable subordination, sharp martingale inequalities and applications
AI总结：
本文提出一种新方法，在可预测从属下获得鞅的尖锐Lp估计，通过量化并补偿Bellman函数中连续与跳跃贡献的缺陷，显著改进了Hamming立方体和Z^n上Riesz向量的显式无维界。
AI中文摘要：
我们引入了一种新方法，用于在可预测的微分从属类比下获得鞅的尖锐$L^p$估计。通过允许针对相关$p$范围调整连续变化与跳跃变化之间的适当比较，我们在路径wise微分从属失效的情形下保持了尖锐常数。关键思想是同时研究由适当的Bellman函数产生的连续和跳跃贡献。尽管这些贡献不必分别非正，我们量化了它们的缺陷，并表明它们在可预测层面上相互补偿。这种补偿机制受到作者早期工作的启发。作为应用，我们显著改进了Hamming立方体和$\mathbb{Z}^n$上Riesz向量的显式无维界。
英文摘要：
We introduce a new method for obtaining sharp $L^p$ estimates for martingales under predictable analogues of differential subordination. By allowing suitable comparisons between continuous and jump variation adapted to the relevant range of $p$, we retain sharp constants in settings where pathwise differential subordination fails. The key idea is to study together the continuous and jump contributions arising from the appropriate Bellman functions. Although these contributions need not be nonpositive separately, we quantify their defects and show that they compensate at the predictable level. This compensation mechanism is inspired by the author's earlier work. As an application, we substantially improve the explicit dimension-free bounds for the Riesz vectors on the Hamming cube and on $\mathbb{Z}^n$.
