论文标题
Haar Martingale变换及其应用的最佳范围
Optimal range of Haar martingale transforms and its applications
论文作者
论文摘要
令$（\ Mathcal {f} _n）_ {n \ ge 0} $为$ [0,1] $上的标准二元过滤。令$ \ mathbb { = 0 $。我们介绍了\ begin {align*} tf = \ sum_ {m = 0}^\ infty \ left（\ mathbb {e} _ { F- \ Mathbb {作为一个应用程序，对于$ [0,1] $上的给定对称功能空间$ e $，我们确定对称空间$ \ MATHCAL {S} _e $，最佳Banach对称范围的Martingale Transforms/HAAR基础预测作用于$ E $。
Let $(\mathcal{F}_n)_{n\ge 0}$ be the standard dyadic filtration on $[0,1]$. Let $\mathbb{E}_{\mathcal{F}_n}$ be the conditional expectation from $ L_1=L_1[0,1]$ onto $\mathcal{F} _n$, $n\ge 0$, and let $\mathbb{E}_{\mathcal{F} _{-1}} =0$. We present the sharp estimate for the distribution function of the martingale transform $T$ defined by \begin{align*} Tf=\sum_{m=0}^\infty \left( \mathbb{E}_{\mathcal{F}_{2m}} f-\mathbb{E}_{\mathcal{F}_{2m-1}}f \right), ~f\in L_1, \end{align*} in terms of the classical Calderón operator. As an application, for a given symmetric function space $E$ on $[0,1]$, we identify the symmetric space $\mathcal{S}_E$, the optimal Banach symmetric range of martingale transforms/Haar basis projections acting on $E$.
