A matrix weighted $T1$ theorem for matrix kernelled Calderon Zygmund operators - I

Abstract

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.

This paper has been withdrawn, and has been split into the following two papers: arXiv:1508.02474 and arXiv:1507.04032

References in corpus (2)

• Linear bound for the dyadic paraproduct on weighted Lebesgue space $L_2(w)$
• Operator-valued dyadic BMO spaces

Cited by in corpus (2)

• Uniform sparse domination of singular integrals via dyadic shifts
• Matrix $A_p$ weights, degenerate Sobolev spaces, and mappings of finite distortion