Sharp spectral multipliers for operators satisfying generalized Gaussian estimates

Adam Sikora*, Lixin Yan, Xiaohua Yao

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    12 Citations (Scopus)

    Abstract

    Let L be a non-negative self-adjoint operator acting on L2(X) where X is a space of homogeneous type. Assume that L generates a holomorphic semigroup e-tL which satisfies generalized m-th order Gaussian estimates. In this article, we study singular and dyadically supported spectral multipliers for abstract self-adjoint operators. We show that in this setting sharp spectral multiplier results follow from Plancherel or Stein-Tomas type estimates. These results are applicable to spectral multipliers for a large class of operators including m-th order elliptic differential operators with constant coefficients, biharmonic operators with rough potentials and Laplace type operators acting on fractals.

    Original languageEnglish
    Pages (from-to)368-409
    Number of pages42
    JournalJournal of Functional Analysis
    Volume266
    Issue number1
    DOIs
    Publication statusPublished - 1 Jan 2014

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