Boundedness of dyadic paraproducts on matrix weighted $L^p$

TL;DR

This paper proves that dyadic paraproducts with BMO functions are bounded on matrix weighted $L^p$ spaces when the weight satisfies the matrix A_p condition, extending scalar results to the matrix setting.

Contribution

It establishes the boundedness of dyadic paraproducts on matrix weighted $L^p$ spaces, a significant extension of classical scalar weighted inequalities to the matrix context.

Findings

Dyadic paraproducts are bounded on matrix weighted $L^p$ spaces.

Boundedness holds under the matrix A_p weight condition.

Extends scalar weighted inequalities to matrix weights.

Abstract

In this paper, we show that dyadic paraproducts $\pi_b$ with $b$ in dyadic BMO are bounded on matrix weighted $L^p(W)$ if $W$ is a matrix $\text{A}_p$ weight.