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2019 Commutators of multiparameter flag singular integrals and applications
Xuan Thinh Duong, Ji Li, Yumeng Ou, Jill Pipher, Brett D. Wick
Anal. PDE 12(5): 1325-1355 (2019). DOI: 10.2140/apde.2019.12.1325

Abstract

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.

Citation

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Xuan Thinh Duong. Ji Li. Yumeng Ou. Jill Pipher. Brett D. Wick. "Commutators of multiparameter flag singular integrals and applications." Anal. PDE 12 (5) 1325 - 1355, 2019. https://doi.org/10.2140/apde.2019.12.1325

Information

Received: 19 February 2018; Revised: 24 July 2018; Accepted: 16 September 2018; Published: 2019
First available in Project Euclid: 5 January 2019

zbMATH: 1405.42041
MathSciNet: MR3892406
Digital Object Identifier: 10.2140/apde.2019.12.1325

Subjects:
Primary: 42B20, 42B30, 42B35

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.12 • No. 5 • 2019
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