论文标题
DOOB对树木相干随机变量和最大运算符的估计
Doob's estimate for coherent random variables and maximal operators on trees
论文作者
论文摘要
令$ξ$为在$（ω，\ Mathcal {f}，\ Mathbb {p}）$上定义的可集成随机变量。 fix $ k \ in \ mathbb {z} _+$，让$ \ {\ mathcal {g} _ {i}^{j}^{j} \} _ {1 \ le i \ le i \ le i \ le i \ le i \ le j \ le j \ le j \ le k} $是$ - $ fields $ nisus $ - $σ $ \ {\ Mathcal {g} _ {i}^{j} \} _ {1 \ le i \ le n} $是每个$ j \ in \ in \ in \ {1,2，\ dots，\ dots，k \} $的过滤。 在本文中，我们解释了对相应相干矢量的最大函数的分析与无hardy-little-Little Wood Maximal Operator的最大函数的分析与基本组合特性之间的基本联系。遵循Grafakos，Kinnunen和Montgomery-Smith的经典方法，我们建立了著名的Doob的最大估计值的适当版本。
Let $ξ$ be an integrable random variable defined on $(Ω, \mathcal{F}, \mathbb{P})$. Fix $k\in \mathbb{Z}_+$ and let $\{\mathcal{G}_{i}^{j}\}_{1\le i \le n, 1\le j \le k}$ be a reference family of sub-$σ$-fields of $\mathcal{F}$, such that $\{\mathcal{G}_{i}^{j}\}_{1\le i \le n}$ is a filtration for each $j\in \{1,2,\dots,k\}$. In this article we explain the underlying connection between the analysis of the maximal functions of the corresponding coherent vector and basic combinatorial properties of the uncentered Hardy-Littlewood maximal operator. Following a classical approach of Grafakos, Kinnunen and Montgomery-Smith, we establish an appropriate version of the celebrated Doob's maximal estimate.
