Restriction estimates, sharp spectral multipliers and endpoint estimates for Bochner-Riesz means

Peng Chen*, El Maati Ouhabaz, Adam Sikora, Lixin Yan

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    15 Citations (Scopus)

    Abstract

    We consider abstract non-negative self-adjoint operators on L2(X) which satisfy the finite-speed propagation property for the corresponding wave equation. For such operators, we introduce a restriction type condition, which in the case of the standard Laplace operator is equivalent to (p, 2) restriction estimate of Stein and Tomas. Next, we show that in the considered abstract setting, our restriction type condition implies sharp spectral multipliers and endpoint estimates for the Bochner-Riesz summability. We also observe that this restriction estimate holds for operators satisfying dispersive or Strichartz estimates. We obtain new spectral multiplier results for several second order differential operators and recover some known results. Our examples include Schrödinger operators with inverse square potentials on Rn, the harmonic oscillator, elliptic operators on compact manifolds, and Schr¨odinger operators on asymptotically conic manifolds.

    Original languageEnglish
    Pages (from-to)219-283
    Number of pages65
    JournalJournal d'Analyse Mathematique
    Volume129
    Issue number1
    DOIs
    Publication statusPublished - Jul 2016

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