Vol. 12, No. 5, 2019

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

Volume 13
Issue 4, 945–1268
Issue 3, 627–944
Issue 2, 317–625
Issue 1, 1–316

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
Editorial Board
Editors’ Interests
Scientific Advantages
Submission Guidelines
Submission Form
Editorial Login
Ethics Statement
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
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.

PDF Access Denied

However, your active subscription may be available on Project Euclid at

We have not been able to recognize your IP address as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

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