Analysis & PDE

  • Anal. PDE
  • Volume 12, Number 5 (2019), 1325-1355.

Commutators of multiparameter flag singular integrals and applications

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

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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.

Article information

Source
Anal. PDE, Volume 12, Number 5 (2019), 1325-1355.

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

Permanent link to this document
https://projecteuclid.org/euclid.apde/1546657235

Digital Object Identifier
doi:10.2140/apde.2019.12.1325

Mathematical Reviews number (MathSciNet)
MR3892406

Zentralblatt MATH identifier
1405.42041

Subjects
Primary: 42B30: $H^p$-spaces 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42B35: Function spaces arising in harmonic analysis

Keywords
multiparameter flag setting flag commutator Hardy space BMO space div-curl lemma

Citation

Duong, Xuan Thinh; Li, Ji; Ou, Yumeng; Pipher, Jill; Wick, Brett D. Commutators of multiparameter flag singular integrals and applications. Anal. PDE 12 (2019), no. 5, 1325--1355. doi:10.2140/apde.2019.12.1325. https://projecteuclid.org/euclid.apde/1546657235


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