Recent results on matrix weighted norm inequalities

TL;DR

This paper reviews recent advances in matrix weighted norm inequalities, focusing on convex body sparse domination, extrapolation, and factorization, and compares these with classical scalar weighted results.

Contribution

It provides a comprehensive overview of recent developments in matrix weights, highlighting new techniques and results in the field.

Findings

Advances in convex body sparse domination for singular integrals

Extensions of Rubio de Francia extrapolation to matrix weights

Jones factorization applied to matrix weighted inequalities

Abstract

In this paper we give an overview of recent work on matrix weights, with particular emphasis on convex body sparse domination for singular integrals, Rubio de Francia extrapolation, and Jones factorization. To provide context and motivation, we survey the comparable results in the scalar weighted case.