Matrix weighted norm inequalities for commutators and paraproducts with matrix symbols
(2017) In Journal of the London Mathematical Society 96(1). p.243-270- 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:
https://lup.lub.lu.se/record/a094bbf1-c568-42aa-b7ea-305bcf03112f
- author
- Isralowitz, Joshua LU ; Kwon, Hyun Kyoung and Pott, Sandra LU
- organization
- publishing date
- 2017-08
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Journal of the London Mathematical Society
- volume
- 96
- issue
- 1
- pages
- 243 - 270
- publisher
- Oxford University Press
- external identifiers
-
- scopus:85021805965
- wos:000415345500013
- 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
- 2024-10-01 07:12:01
@article{a094bbf1-c568-42aa-b7ea-305bcf03112f, abstract = {{<p>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.</p>}}, author = {{Isralowitz, Joshua and Kwon, Hyun Kyoung and Pott, Sandra}}, issn = {{0024-6107}}, language = {{eng}}, number = {{1}}, pages = {{243--270}}, 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}}, doi = {{10.1112/jlms.12053}}, volume = {{96}}, year = {{2017}}, }