Trigonometric chaos and Xp inequalities II. Xp inequalities in group von Neumann algebras

In the line of previous work by Naor, we establish new forms of metric Xp inequalities in group algebras under very general assumptions. Our results’ applicability goes beyond the previously known setting in two directions. In the first place, we find continuous forms of the Xp inequality in the n-dimensional torus. Second, we consider transferred forms of the sharp scalar valued metric Xp inequality in the von Neumann algebra L(G) of a discrete group 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 Lp spaces. © 2025 by the University of Illinois Urbana-Champaign.