A noncommutative version of the John-Nirenberg theorem

TL;DR

This paper extends the classical John-Nirenberg theorem to the noncommutative setting of von Neumann algebras, providing new insights into noncommutative harmonic analysis and large deviation inequalities.

Contribution

It introduces a noncommutative version of the John-Nirenberg theorem for nontracial filtrations of von Neumann algebras, a novel theoretical advancement.

Findings

Established a noncommutative John-Nirenberg theorem

Derived a large deviation inequality for noncommutative BMO spaces

Extended classical harmonic analysis results to the noncommutative setting

Abstract

We prove a noncommutative version of the John-Nirenberg theorem for nontracial filtrations of von Neumann algebras. As an application, we obtain an analogue of the classical large deviation inequality for elements of the associated $BMO$ space.