Vol. 12, No. 5, 2019

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 5, 1501–1870
Issue 4, 1127–1500
Issue 3, 757–1126
Issue 2, 379–756
Issue 1, 1–377

Volume 16, 10 issues

Volume 15, 8 issues

Volume 14, 8 issues

Volume 13, 8 issues

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
Editors' interests
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Author index
To appear
Other MSP journals
Commutators of multiparameter flag singular integrals and applications

Xuan Thinh Duong, Ji Li, Yumeng Ou, Jill Pipher and Brett D. Wick

Vol. 12 (2019), No. 5, 1325–1355

We introduce the iterated commutator for the Riesz transforms in the multiparameter flag setting, and prove the upper bound of this commutator with respect to the symbol b in the flag BMO space. Our methods require the techniques of semigroups, harmonic functions and multiparameter flag Littlewood–Paley analysis. We also introduce the big commutator in this multiparameter flag setting and prove the upper bound with symbol b in the flag little bmo space by establishing the “exponential-logarithmic” bridge between this flag little bmo space and the Muckenhoupt Ap weights with flag structure. As an application, we establish the div-curl lemmas with respect to the appropriate Hardy spaces in the multiparameter flag setting.

multiparameter flag setting, flag commutator, Hardy space, BMO space, div-curl lemma
Mathematical Subject Classification 2010
Primary: 42B30, 42B20, 42B35
Received: 19 February 2018
Revised: 24 July 2018
Accepted: 16 September 2018
Published: 15 December 2018
Xuan Thinh Duong
Department of Mathematics
Macquarie University
Ji Li
Department of Mathematics
Macquarie University
Yumeng Ou
Department of Mathematics
Baruch College
The City University of New York
New York, NY
United States
Jill Pipher
Department of Mathematics
Brown University
Providence, RI
United States
Brett D. Wick
Department of Mathematics
Washington University–St. Louis
St. Louis, MO
United States