Asymmetric Burkholder inequalities in noncommutative symmetric spaces

TL;DR

This paper extends noncommutative Burkholder inequalities to asymmetric symmetric operator spaces using complex interpolation and duality, also providing asymmetric Johnson-Schechtman inequalities.

Contribution

It introduces asymmetric versions of noncommutative Burkholder and Johnson-Schechtman inequalities with new interpolation techniques.

Findings

Established noncommutative Burkholder inequalities with asymmetric diagonals

Developed a new complex interpolation result for asymmetric vector valued spaces

Provided asymmetric versions of Johnson-Schechtman inequalities

Abstract

In this paper, we establish noncommutative Burkholder inequalities with asymmetric diagonals in symmetric operator spaces. Our proof mainly relies on a new complex interpolation result on asymmetric vector valued spaces and a duality approach. We include as well the asymmetric versions of noncommutative Johnson-Schechtman inequalities.