论文标题
John-Nirenberg非交通柱BMO和Lipschitz Martingales的不平等现象
John-Nirenberg inequalities for noncommutative column BMO and Lipschitz martingales
论文作者
论文摘要
在本文中，我们继续研究了非交通性的玛格丽尔环境中BMO/Lipschitz空间的John-Nirenberg定理。从经典案例中提出的那样，发现了一种未进行的非交换性``停止时间''参数，以获得John-nirenberg Theorem的分布函数不平等的形式。这不仅提供了另一种方法，而无需使用二元性和插值来实现二重性和插值，以实现空间的结果， $ {λ^{C}_β}（\ Mathcal {M}）$，但也允许我们找到约翰 - 尼尔贝格的所需版本的空间$ \ MATHCAL {BMO}^C（\ MATHCAL M）$和$ {\ MATHCAL L^{c} $ \ Cite {Ref5，Ref3}的两个开放性问题，我们表明Lipschitz空间也是通过对称原子定义的非共同空间的双重空间。
In this paper, we continue the study of John-Nirenberg theorems for BMO/Lipschitz spaces in the noncommutative martingale setting. As conjectured from the classical case, a desired noncommutative ``stopping time" argument was discovered to obtain the distribution function inequality form of John-Nirenberg theorem. This not only provides another approach without using duality and interpolation to the results for spaces $\mathsf{bmo}^c(\mathcal M)$ and ${Λ^{c}_β}(\mathcal{M})$, but also allows us to find the desired version of John-Nirenberg inequalities for spaces $\mathcal{BMO}^c(\mathcal M)$ and ${\mathcal L^{c}_β}(\mathcal{M})$. And thus we solve two open questions after \cite{ref5, ref3}. As an application, we show that Lipschitz space is also the dual space of noncommutative Hardy space defined via symmetric atoms. Finally, our results for ${\mathcal L^{c}_β}(\mathcal{M})$ as well as the approach seem new even going back to the classical setting.
