Besov and Triebel-Lizorkin spaces associated to Hermite operators

The Anh Bui*, Xuan Thinh Duong

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    17 Citations (Scopus)

    Abstract

    Consider the Hermite operator (Formula presented.) on the Euclidean space (Formula presented.). The main aim of this article is to develop a theory of homogeneous and inhomogeneous Besov and Triebel–Lizorkin spaces associated to the Hermite operator. Our inhomogeneous Besov and Triebel–Lizorkin spaces are different from those introduced by Petrushev and Xu (J Fourier Anal Appl 14, 372–414 2008). As applications, we show the boundedness of negative powers and spectral multipliers of the Hermite operators on some appropriate Besov and Triebel–Lizorkin spaces.

    Original languageEnglish
    Pages (from-to)405-448
    Number of pages44
    JournalJournal of Fourier Analysis and Applications
    Volume21
    Issue number2
    DOIs
    Publication statusPublished - Apr 2015

    Keywords

    • Besov space
    • Hermite operator
    • Molecular decomposition
    • Triebel–Lizorkin space

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