Compactness of commutator of Riesz transforms in the two weight setting

Michael Lacey, Ji Li*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    1 Citation (Scopus)


    We characterize the compactness of commutators in the Bloom setting. Namely, for a suitably non-degenerate Calderón–Zygmund operator T, and a pair of weights σ,ω∈Ap, the commutator [T,b] is compact from Lp(σ)→Lp(ω) if and only if b∈VMOν, where ν=(σ/ω)1/p. This extends the work of the first author, Holmes and Wick. The weighted VMO spaces are different from the classical VMO space. In dimension d=1, compactly supported and smooth functions are dense in VMOν, but this need not hold in dimensions d≥2. Moreover, the commutator in the product setting with respect to little VMO space is also investigated.

    Original languageEnglish
    Article number125869
    Pages (from-to)1-11
    Number of pages11
    JournalJournal of Mathematical Analysis and Applications
    Issue number1
    Publication statusPublished - 1 Apr 2022


    • Commutator
    • Two weight
    • Compactness
    • Riesz transform


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