A Study of the Matrix Carleson Embedding Theorem with Applications to Sparse Operators
Publication Date
2016
Description
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 H-1-BMO duality. Along the way, we establish boundedness results about maximal functions associated to matrix A(2) weights and duality results concerning H-1 and BMO sequence spaces in the matrix setting. As an application, we then use this Carleson Embedding Theorem to show that if S is a sparse operator, then the operator norm of S on L-2 (W) satisfies parallel to S parallel to(2)(L2(W)-> L)((W)) less than or similar to [W](A2)(3/2), for every matrix A(2) weight W. (C) 2015 Elsevier Inc. All rights reserved.
Journal
Journal of Mathematical Analysis and Applications
Volume
435
Issue
1
First Page
229
Last Page
243
Department
Mathematics
Link to Published Version
DOI
10.1016/j.jmaa.2015.10.023
Recommended Citation
Bickel, Kelly and Wick, Brett D.. "A Study of the Matrix Carleson Embedding Theorem with Applications to Sparse Operators." Journal of Mathematical Analysis and Applications (2016) : 229-243.