Bounds on the maximal bochner-riesz means for elliptic operators

Peng Chen*, Sanghyuk Lee, Adam Sikora, Lixin Yan

*Corresponding author for this work

    Research output: Contribution to journalArticle

    1 Citation (Scopus)

    Abstract

    We investigate Lp boundedness of the maximal Bochner-Riesz means for self-adjoint operators of elliptic-type. Assuming the finite speed of propagation for the associated wave operator, from the restriction-type estimates we establish the sharp Lp boundedness of the maximal Bochner-Riesz means for the elliptic operators. As applications, we obtain the sharp Lp maximal bounds for the Schrödinger operators on asymptotically conic manifolds, elliptic operators on compact manifolds, or the Hermite operator and its perturbations on ℝn .
    Original languageEnglish
    Pages (from-to)3793-3828
    Number of pages36
    JournalTransactions of the American Mathematical Society
    Volume373
    Issue number6
    Early online date2 Mar 2020
    DOIs
    Publication statusPublished - Jun 2020

    Keywords

    • Maximal Bochner-Riesz means
    • non-negative self-adjoint operators
    • finite speed propagation property
    • elliptic-type estimates
    • restriction-type conditions

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