Compactness of Riesz transform commutator associated with Bessel operators

Xuan Thinh Duong, Ji Li, Suzhen Mao, Huoxiong Wu, Dongyong Yang*

*Corresponding author for this work

    Research output: Contribution to journalArticle

    2 Citations (Scopus)

    Abstract

    Let λ > 0 and Δλ:=−d2dx2−2λxddx be the Bessel operator on R+:= (0,∞). We first introduce and obtain an equivalent characterization of CMO(R+, xdx). By this equivalent characterization and by establishing a new version of the Fréchet-Kolmogorov theorem in the Bessel setting, we further prove that a function b ∈ BMO(R+, xdx) is in CMO(R+, xdx) if and only if the Riesz transform commutator xxxx is compact on Lp(R+, xdx) for all p ∈ (1,∞).

    Original languageEnglish
    Pages (from-to)639-673
    Number of pages35
    JournalJournal d'Analyse Mathematique
    Volume135
    Issue number2
    DOIs
    Publication statusPublished - 1 Jun 2018

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