# Weak endpoint bounds for matrix weights

## TL;DR

This paper establishes new quantitative endpoint bounds for matrix weights in harmonic analysis, specifically for maximal operators, Calderón-Zygmund operators, and their commutators under $A_1$ matrix weights.

## Contribution

It provides the first quantitative matrix weighted endpoint estimates for these operators when the matrix weight belongs to the $A_1$ class.

## Key findings

- Proves endpoint bounds for matrix weighted Hardy-Littlewood maximal operator.
- Establishes bounds for Calderón-Zygmund operators with matrix weights.
- Analyzes commutators of CZOs with scalar BMO functions under matrix weights.

## Abstract

We prove quantitative matrix weighted endpoint estimates for the matrix weighted Hardy-Littlewood maximal operator, Calder\'on-Zygmund operators, and commutators of CZOs with scalar BMO functions, when the matrix weight is in the class $A_1$ introduced by M.~Frazier and S.~Roudenko.