Higher-order Riesz transforms of Hermite operators on new Besov and Triebel–Lizorkin spaces

The Anh Bui, Xuan Thinh Duong*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    1 Citation (Scopus)

    Abstract

    Consider the Hermite operator H=−Δ+|x|2 on the Euclidean space Rn. The aim of this article is to prove the boundedness of higher-order Riesz trnsforms on appropriate Besov and Triebel–Lizorkin spaces. As an application, we prove certain regularity estimates of second-order elliptic equations in divergence form with the oscillator perturbations.

    Original languageEnglish
    Pages (from-to)85-120
    Number of pages36
    JournalConstructive Approximation
    Volume53
    Issue number1
    Early online date8 Jan 2020
    DOIs
    Publication statusPublished - Feb 2021

    Keywords

    • Hermite operator
    • Higher order Riesz transforms
    • Besov space
    • Triebel–Lizorkin space

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