Compactness of Riesz transform commutator on stratified Lie groups

Peng Chen, Xuan Thinh Duong, Ji Li, Qingyan Wu*

*Corresponding author for this work

    Research output: Contribution to journalArticle

    1 Citation (Scopus)

    Abstract

    Let G be a stratified Lie group and {Xj}1≤j≤n a basis for the left-invariant vector fields of degree one on G. Let Δ=∑j=1 nXj 2 be the sub-Laplacian on G. The jth Riesz transform on G is defined by Rj:=Xj(−Δ)-1/2, 1≤j≤n. In this paper, we provide a concrete construction of the "twisted truncated sector" which is related to the pointwise lower bound of the kernel of Rj on G. Then we obtain the characterisation of compactness of the commutators of Rj with a function b∈VMO(G), the space of functions with vanishing mean oscillation on G.

    Original languageEnglish
    Pages (from-to)1639-1676
    Number of pages38
    JournalJournal of Functional Analysis
    Volume277
    Issue number6
    DOIs
    Publication statusPublished - 15 Sep 2019

    Keywords

    • Stratified Lie groups
    • Riesz transforms
    • VMO space
    • Commutator

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