论文标题
非交通性的原子分解
Atomic decompositions for noncommutative martingales
论文作者
论文摘要
我们证明了一种原子类型的分解，用于使用代数原子作为构建块的明确建设性方法，用于所有$ 0 <p <2 $的非交通型Martingale Hardy Space $ \ h_p $。使用这种基本结构，我们获得了所有$ 0 <p <1，$的原子分解的薄弱形式，并提供了$ p = 1 $的原子分解的建设性证明。我们还研究$（p，\ 8）_c $ -ATOMS，并表明每$（P，2）_c $ -atom可以分解为$（p，\ 8）_c $ -atoms的总和；因此，对于每$ 0 <p \ le 1 $，$（p，q）_c $ - 原子会导致所有$ 2 \ le q \ le \ le \ 8 $都会到达相同的原子空间。作为应用程序，我们通过原子分解的弱形式获得了非交通性martingale hardy空间$ \ h_p $（$ 0 <p <1 $）的表征。我们的建设性方法也可以应用于证明一些急剧的不平等现象。
We prove an atomic type decomposition for the noncommutative martingale Hardy space $\h_p$ for all $0<p<2$ by an explicit constructive method using algebraic atoms as building blocks. Using this elementary construction, we obtain a weak form of the atomic decomposition of $\h_p$ for all $0< p < 1,$ and provide a constructive proof of the atomic decomposition for $p=1$. We also study $(p,\8)_c$-atoms, and show that every $(p,2)_c$-atom can be decomposed into a sum of $(p,\8)_c$-atoms; consequently, for every $0<p\le 1$, the $(p,q)_c$-atoms lead to the same atomic space for all $2\le q\le\8$. As applications, we obtain a characterization of the dual space of the noncommutative martingale Hardy space $\h_p$ ($0<p<1$) as a noncommutative Lipschitz space via the weak form of the atomic decomposition. Our constructive method can also be applied to proving some sharp martingale inequalities.
