Weak-type interpolation for noncommutative maximal operators

TL;DR

This paper establishes a Boyd-type interpolation theorem for noncommutative maximal operators of restricted weak type, providing a new version of the noncommutative Marcinkiewicz interpolation theorem with optimal constants.

Contribution

It introduces a Boyd-type interpolation result for noncommutative maximal operators, answering an open question and refining existing theorems with optimal constants.

Findings

Proves a Boyd-type interpolation theorem for noncommutative maximal operators

Provides a restricted weak type version of the noncommutative Marcinkiewicz theorem

Achieves interpolation constants of optimal order

Abstract

We prove a Boyd-type interpolation result for noncommutative maximal operators of restricted weak type. Our result positively answers an open question posed recently by Bekjan, Chen and Osekowski. As a special case, we find a restricted weak type version of the noncommutative Marcinkiewicz interpolation theorem, due to Junge and Xu, with interpolation constant of optimal order.