论文标题
三角混乱和$ \ m m i {x} _p $ inboralities ii- $ \ mathrm {x} _p $不平等现象von neumann代数
Trigonometric chaos and $\mathrm{X}_p$ inequalities II -- $\mathrm{X}_p$ inequalities in group von Neumann algebras
论文作者
论文摘要
在NAOR先前的工作中，我们建立了新形式的公制$ \ mathrm {x} _p $在非常一般的假设下组代数的不平等现象。我们的结果的适用性超出了两个方向上以前已知的设置。首先，我们找到了$ \ mathrm {x} _p $不平等的连续形式。其次，我们考虑了von neumann algebra $ \ mathcal {l}（\ mathrm {g}）$的尖锐标量值$ \ mathrm {x} _p $不平等的转移形式。作为我们结果的副产品，在非共同$ L_P $空间的背景下，探索了一些度量后果及其与BANACH空间的Bi-Lipschitz非舒适性的关系。
In the line of previous work by Naor, we establish new forms of metric $\mathrm{X}_p$ inequalities in group algebras under very general assumptions. Our results' applicability goes beyond the previously known setting in two directions. In first place, we find continuous forms of the $\mathrm{X}_p$ inequality in the $n$-dimensional torus. Second, we consider transferred forms of the sharp scalar valued metric $\mathrm{X}_p$ inequality in the von Neumann algebra $\mathcal{L}(\mathrm{G})$ of a discrete group $\mathrm{G}$. As a byproduct of our results, some metric consequences and their relation with bi-Lipschitz nonembeddability of Banach spaces are explored in the context of noncommutative $L_p$ spaces.
