Sharp $p/\log p$ Bounds for Metric $X_p$ Inequalities and Arbitrary Rademacher Chaos

Naor proved that $L_p$ satisfies the metric $X_p$ inequality with the sharp scaling parameter and asked for the optimal dependence of its constant on $p$. The best previously known upper bound was $O(p^4/\log p)$, while first-degree chaos gives a lower bound of order $p/\log p$. We prove the matchin