Sharp Metric Cotype Inequalities for $L_1$ via Nonlinear Cut Smoothing

Qingjin Cheng, Yue Wang, Bo Xiang

For every $1\le p<\infty$ and even integer $m\ge 4$, we determine the optimal order of the $p$-moment torus inequality for $L_1$: it is $m^p{n}^{(1-p/2{)}_{+}}+n$, with comparison cons…