Commutators on weighted Morrey spaces on spaces of homogeneous type

Ruming Gong, Ji Li*, Elodie Pozzi, Manasa N. Vempati

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    Abstract

    In this paper, we study the boundedness and compactness of the commutator of Calderón- Zygmund operators T on spaces of homogeneous type (X, d, μ) in the sense of Coifman and Weiss. More precisely, we show that the commutator [b, T] is bounded on the weighted Morrey space Lωp,k(X) with κ ∈ (0, 1) and ω ∈ Ap(X), 1 < p < ∞, if and only if b is in the BMO space. We also prove that the commutator [b, T] is compact on the same weighted Morrey space if and only if b belongs to the VMO space. We note that there is no extra assumptions on the quasimetric d and the doubling measure μ.

    Original languageEnglish
    Pages (from-to)305-334
    Number of pages30
    JournalAnalysis and Geometry in Metric Spaces
    Volume8
    Issue number1
    DOIs
    Publication statusPublished - 2020

    Bibliographical note

    Copyright the Author(s) 2020. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

    Keywords

    • commutator
    • compact operator
    • BMO space
    • VMO space
    • weighted Morrey space
    • space of homogeneous type

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