Weighted weak $(1,1)$ estimate for non-commutative square function

Abstract

In this article, we consider weighted weak type $(1,1)$ inequality for certain square function associated to differences of ball averages and martingale in the non-commutative setting. This establishes a weighted version of main result of \cite{hong2021noncommutative}.

15 pages, typos fixed, more details are added, to appear in Bulletin of the London Mathematical Society