论文标题
Martingale类型，Gamlen-Gaudet结构和贪婪的算法
Martingale Type, the Gamlen-Gaudet Construction and a Greedy Algorithm
论文作者
论文摘要
在本文中，我们确定了那些过滤的概率空间$（ω，\，\ Mathcal {f}，\，\，\ left（\ Mathcal {f} _n \ right），\，\ Mathbb {p}）$已经确定了Banach Space $ x $ x $的martingale类型。我们隔离过滤$（\ MATHCAL {f} _n）纯原子$σ$ -Algebras的内在条件 \ [ \ | f \ | _ {l^p（ω，\，x）}^p \ leq c^p \ left（\ | \ | \ Mathbb {E} f \ |^p_ {l^p（ω，\，x）} \ right），\ qquad f \ in l^p（ω，x）\]暗示Banach Space $ x $是Martingale type $ p $。我们的论文补充了\ mbox {g。 Pisier's}调查\ cite {Pisier1975}，并继续由S. Geiss和第二名的作者在\ cite {geiss2008}中命名为作者。
In the present paper we identify those filtered probability spaces $(Ω,\, \mathcal{F},\, \left(\mathcal{F}_n\right),\, \mathbb{P})$ that determine already the martingale type of a Banach space $X$. We isolate intrinsic conditions on the filtration $(\mathcal{F}_n)$ of purely atomic $σ$-algebras which determine that the upper $\ell^p$ estimates \[ \|f\|_{L^p(Ω,\, X)}^p\leq C^p\left( \|\mathbb{E} f|\mathcal{F}_0\|^p_{L^p(Ω,\, X)}+\sum_{n=1}^{\infty} \|Δ_n f\|^p_{L^p(Ω,\, X)}\right),\qquad f\in L^p(Ω,X)\] imply that the Banach space $X$ is of martingale type $p$. Our paper complements \mbox{G. Pisier's} investigation \cite{Pisier1975} and continues the work by S. Geiss and second named author in \cite{Geiss2008}.
