Commutators in the two scalar and matrix weighted setting
(2022) In Journal of the London Mathematical Society 106(1). p.1-26- Abstract
In this paper, we approach the two weighted boundedness of commutators via matrix weights. This approach provides both a sufficient and a necessary condition for the two weighted boundedness of commutators with an arbitrary linear operator in terms of one matrix weighted norm inequalities for this operator. Furthermore, using this approach, we surprisingly provide conditions that almost characterize the two matrix weighted boundedness of commutators with CZOs and completely arbitrary matrix weights, which is even new in the fully scalar one weighted setting. Finally, our method allows us to extend the two weighted Holmes/Lacey/Wick results to the fully matrix setting (two matrix weights and a matrix symbol), completing a line of... (More)
In this paper, we approach the two weighted boundedness of commutators via matrix weights. This approach provides both a sufficient and a necessary condition for the two weighted boundedness of commutators with an arbitrary linear operator in terms of one matrix weighted norm inequalities for this operator. Furthermore, using this approach, we surprisingly provide conditions that almost characterize the two matrix weighted boundedness of commutators with CZOs and completely arbitrary matrix weights, which is even new in the fully scalar one weighted setting. Finally, our method allows us to extend the two weighted Holmes/Lacey/Wick results to the fully matrix setting (two matrix weights and a matrix symbol), completing a line of research initiated by the first two authors.
(Less)
- author
- Isralowitz, Joshua LU ; Pott, Sandra LU and Treil, Sergei
- organization
- publishing date
- 2022-07-01
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Journal of the London Mathematical Society
- volume
- 106
- issue
- 1
- pages
- 26 pages
- publisher
- Oxford University Press
- external identifiers
-
- scopus:85132360074
- ISSN
- 0024-6107
- DOI
- 10.1112/jlms.12560
- language
- English
- LU publication?
- yes
- id
- 03e744d0-eb14-48c1-a53f-333e0f8e75a4
- date added to LUP
- 2022-09-23 10:14:17
- date last changed
- 2022-09-23 10:14:17
@article{03e744d0-eb14-48c1-a53f-333e0f8e75a4,
abstract = {{<p>In this paper, we approach the two weighted boundedness of commutators via matrix weights. This approach provides both a sufficient and a necessary condition for the two weighted boundedness of commutators with an arbitrary linear operator in terms of one matrix weighted norm inequalities for this operator. Furthermore, using this approach, we surprisingly provide conditions that almost characterize the two matrix weighted boundedness of commutators with CZOs and completely arbitrary matrix weights, which is even new in the fully scalar one weighted setting. Finally, our method allows us to extend the two weighted Holmes/Lacey/Wick results to the fully matrix setting (two matrix weights and a matrix symbol), completing a line of research initiated by the first two authors.</p>}},
author = {{Isralowitz, Joshua and Pott, Sandra and Treil, Sergei}},
issn = {{0024-6107}},
language = {{eng}},
month = {{07}},
number = {{1}},
pages = {{1--26}},
publisher = {{Oxford University Press}},
series = {{Journal of the London Mathematical Society}},
title = {{Commutators in the two scalar and matrix weighted setting}},
url = {{http://dx.doi.org/10.1112/jlms.12560}},
doi = {{10.1112/jlms.12560}},
volume = {{106}},
year = {{2022}},
}