A matrix weighted $T1$ theorem for matrix kernelled Calderon Zygmund   operators - I
  In this series of two papers, we will prove a natural matrix weighted $T1$ theorem for matrix kernelled CZOs. In the current paper, we will prove matrix weighted norm inequalities for matrix symbolled paraproducts via a general matrix weighted Carleson embedding theorem. Along the way, we will also provide a stopping time proof of the identification of $L^p(W)$ as a weighted Triebel-Lizorkin space when $W$ is a matrix A${}_p$ weight. 
Joshua Isralowitz, Hyun Kyoung Kwon, Sandra Pott
math.CA