Triebel–Lizorkin–Morrey spaces associated to Hermite operators

Nguyen Ngoc Trong, Le Xuan Truong*, Tran Tri Dung, Hanh Nguyen Vo

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review


    The aim of this article is to establish molecular decomposition of homogeneous and inhomogeneous Triebel–Lizorkin–Morrey spaces associated to the Hermite operator H≡ - Δ + | x| 2 on the Euclidean space Rn. As applications of the molecular decomposition theory, we show the Triebel–Lizorkin–Morrey boundedness of Riesz potential, Bessel potential and spectral multipliers associated to the operator H. These results generalize the corresponding results in Bui and Duong (J Fourier Anal Appl 21:405–448, 2015).

    Original languageEnglish
    Pages (from-to)527-555
    Number of pages29
    JournalRevista Matematica Complutense
    Issue number2
    Publication statusPublished - May 2020


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


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