The Cauchy integral, bounded and compact commutators

Ji Li, Trang T. T. Nguyen, Lesley A. Ward, Brett D. Wick

    Research output: Contribution to journalArticle

    Abstract

    We study the commutator of the well-known Cauchy integral with a locally integrable function b on R, and establish a characterisation of the BMO space on R via the Lp boundedness of this commutator. Moreover, we also establish a characterisation of the VMO space on R via the compactness of this commutator.
    Original languageEnglish
    Pages (from-to)193-216
    Number of pages24
    JournalStudia Mathematica
    Volume250
    Issue number2
    DOIs
    Publication statusPublished - 2020

    Keywords

    • BMO spaces
    • VMO spaces
    • commutators
    • Cauchy integrals

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  • Cite this

    Li, J., Nguyen, T. T. T., Ward, L. A., & Wick, B. D. (2020). The Cauchy integral, bounded and compact commutators. Studia Mathematica, 250(2), 193-216. https://doi.org/10.4064/sm180715-13-12