Quantitative matrix weighted estimates for certain singular integral operators

TL;DR

This paper develops quantitative weighted matrix estimates for vector-valued singular integral operators, providing new bounds and endpoint estimates using convex body domination techniques.

Contribution

It introduces new convex body domination results and extends weighted matrix estimates to vector-valued singular integrals with various bounds.

Findings

Established strong type (p,p) estimates

Derived endpoint estimates for singular integrals

Provided new Coifman-Fefferman estimates under $A_$ and $C_p$ conditions

Abstract

In this paper quantitative weighted matrix estimates for vector valued extensions of $L^{r'}$-H\"ormander operators and rough singular integrals are studied. Strong type $(p,p)$ estimates, endpoint estimates, and some new results on Coifman-Fefferman estimates assuming $A_\infty$ and $C_p$ condition counterparts are provided. To prove the aforementioned estimates we rely upon some suitable convex body domination results that we settle as well in this paper.