Commutators of multiparameter flag singular integrals and applications

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

    Research output: Contribution to journalArticleResearchpeer-review

    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.

    LanguageEnglish
    Pages1325-1355
    Number of pages31
    JournalAnalysis and PDE
    Volume12
    Issue number5
    DOIs
    Publication statusPublished - 1 Jan 2019

    Fingerprint

    Electric commutators
    Singular Integrals
    Commutator
    Ap Weights
    Muckenhoupt Weights
    BMO Space
    Upper bound
    Harmonic functions
    Riesz Transform
    Curl
    Hardy Space
    Harmonic Functions
    Lemma
    Logarithmic
    Semigroup

    Keywords

    • BMO space
    • Div-curl lemma
    • Flag commutator
    • Hardy space
    • Multiparameter flag setting

    Cite this

    Duong, Xuan Thinh ; Li, Ji ; Ou, Yumeng ; Pipher, Jill ; Wick, Brett D. / Commutators of multiparameter flag singular integrals and applications. In: Analysis and PDE. 2019 ; Vol. 12, No. 5. pp. 1325-1355.
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    Commutators of multiparameter flag singular integrals and applications. / Duong, Xuan Thinh; Li, Ji; Ou, Yumeng; Pipher, Jill; Wick, Brett D.

    In: Analysis and PDE, Vol. 12, No. 5, 01.01.2019, p. 1325-1355.

    Research output: Contribution to journalArticleResearchpeer-review

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    AU - Duong, Xuan Thinh

    AU - Li, Ji

    AU - Ou, Yumeng

    AU - Pipher, Jill

    AU - Wick, Brett D.

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    AB - 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.

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    KW - Div-curl lemma

    KW - Flag commutator

    KW - Hardy space

    KW - Multiparameter flag setting

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