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Matrix weighted norm inequalities for commutators and paraproducts with matrix symbols

Isralowitz, Joshua LU ; Kwon, Hyun Kyoung and Pott, Sandra LU (2017) In Journal of the London Mathematical Society
Abstract

Let B be a locally integrable matrix function, W a matrix Ap weight with 1<p<∞, and T be any of the Riesz transforms. We will characterize the boundedness of the commutator [T,B] on Lp(W) in terms of the membership of B in a natural matrix weighted BMO space. To do this, we will characterize the boundedness of dyadic paraproducts on Lp(W) via a new matrix weighted Carleson embedding theorem. Finally, we will use some of the ideas from these proofs to (among other things) obtain quantitative weighted norm inequalities for these operators and also use them to prove sharp L2 bounds for the Christ/Goldberg matrix weighted maximal function associated with matrix A2 weights.

Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
epub
subject
in
Journal of the London Mathematical Society
publisher
Oxford University Press
external identifiers
  • scopus:85021805965
ISSN
0024-6107
DOI
10.1112/jlms.12053
language
English
LU publication?
yes
id
a094bbf1-c568-42aa-b7ea-305bcf03112f
date added to LUP
2017-07-20 08:40:19
date last changed
2017-07-20 08:40:19
@article{a094bbf1-c568-42aa-b7ea-305bcf03112f,
  abstract     = {<p>Let B be a locally integrable matrix function, W a matrix Ap weight with 1&lt;p&lt;∞, and T be any of the Riesz transforms. We will characterize the boundedness of the commutator [T,B] on Lp(W) in terms of the membership of B in a natural matrix weighted BMO space. To do this, we will characterize the boundedness of dyadic paraproducts on Lp(W) via a new matrix weighted Carleson embedding theorem. Finally, we will use some of the ideas from these proofs to (among other things) obtain quantitative weighted norm inequalities for these operators and also use them to prove sharp L2 bounds for the Christ/Goldberg matrix weighted maximal function associated with matrix A2 weights.</p>},
  author       = {Isralowitz, Joshua and Kwon, Hyun Kyoung and Pott, Sandra},
  issn         = {0024-6107},
  language     = {eng},
  month        = {07},
  publisher    = {Oxford University Press},
  series       = {Journal of the London Mathematical Society},
  title        = {Matrix weighted norm inequalities for commutators and paraproducts with matrix symbols},
  url          = {http://dx.doi.org/10.1112/jlms.12053},
  year         = {2017},
}