Commutators of BMO functions and singular integral operators with non-smooth kernels

Xuan Thinh Duong*, Lixin Yan

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    30 Citations (Scopus)

    Abstract

    Let χ be a space of homogeneous type of infinite measure. Let T be a singular integral operator which is bounded on L p(χ) for some p, 1 < p < ∞. We give a sufficient condition on the kernel of T so that when a function b ∈ BMO(χ), the commutator [b,T](f) = T(bf) - bT(f) is bounded on L p spaces for all p, 1 < p < ∞. Our condition is weaker than the usual Hörmander condition. Applications include L p-boundedness of the commutators of BMO functions and holomorphic functional calculi of Schrödinger operators, and divergence form operators on irregular domains.

    Original languageEnglish
    Pages (from-to)187-200
    Number of pages14
    JournalBulletin of the Australian Mathematical Society
    Volume67
    Issue number2
    Publication statusPublished - Apr 2003

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