A Study of the Matrix Carleson Embedding Theorem with Applications to Sparse Operators

Kelly Bickel, Bucknell University
Brett Wick, Washington University in St. Louis

Abstract

In this paper, we study the dyadic Carleson Embedding Theorem in the matrix weighted setting. We provide two new proofs of this theorem, which highlight connections between the matrix Carleson Embedding Theorem and both maximal functions and H1-BMO duality. Along the way, we establish boundedness results about new maximal functions associated to matrix A2 weights and duality results concerning H1 and BMO sequence spaces in the matrix setting.