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

2014/01/25 by Joshua Isralowitz, Isralowitz, Joshua, Hyun Kyoung Kwon +3 · 1 citation
Mathematics · #42B20 #Advanced Harmonic Analysis Research #Approximation Theory and Sequence Spaces #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory #math.CA #msc:42B20

paper · pdf · doi:10.48550/arxiv.1401.6570

This paper has been withdrawn, and has been split into the following two papers: arXiv:1508.02474 and arXiv:1507.04032

openalex publication_date 2014/01/25 · openalex created_date 2016/06/24 · arxiv created 2017/03/17 · arxiv updated 2017/03/20 · openalex updated_date 2026/07/28

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.

Citations

• Matrix-weighted Besov spaces
• Weighted norm inequalities for the conjugate function and Hilbert transform
• Wavelets and the Angle between Past and Future
• A matrix weighted T1 theorem for matrix kernelled CZOs and a matrix weighted John-Nirenberg theorem

Cited by

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

Related

• Sharp bounds and T1 theorem for Calderón-Zygmund operators with matrix kernel on matrix weighted spaces
• A matrix weighted T1 theorem for matrix kernelled CZOs and a matrix weighted John-Nirenberg theorem
• Bounds for Calderón-Zygmund operators with matrix A₂ weights
• Weak endpoint bounds for matrix weights
• Matrix-weighted estimates beyond Calderón-Zygmund theory