# Majorization, Interpolation and noncommutative Khintchine inequalities

## TL;DR

This paper characterizes quasi-Banach interpolation spaces between Lp spaces, extends known results to non-Banach settings, and applies these findings to noncommutative Khintchine inequalities in symmetric spaces.

## Contribution

It extends interpolation space characterizations to quasi-Banach spaces and applies these to noncommutative Khintchine inequalities, solving a conjecture in the process.

## Key findings

- Characterization of quasi-Banach interpolation spaces for (L_p, L_q)
- Extension of results to non-Banach spaces
- Application to noncommutative Khintchine inequalities in symmetric spaces

## Abstract

Let $0<p<q\leq\infty$ and $\alpha \in (0,\infty]$. We give a characterization of quasi-Banach interpolation spaces for the couple $(L_p(0,\alpha),L_q(0,\alpha))$ in terms of two monotonicity properties, extending known results which mainly dealt with Banach spaces. This enables us to recover recent results of Cwikel and Nilsson on sequence spaces and to solve a conjecture of Levitina, Sukochev and Zanin in the setting of function spaces. We apply the results obtained to characterize symmetric spaces in which the standard forms of the noncommutative Khintchine inequalities hold.