Spectral multiplier theorem and sub-Gaussian heat kernel estimates

Peng Chen, Xixi Lin Colloquium Mathematicum MSC: Primary 42B15; Secondly 42B20, 47F05. DOI: 10.4064/cm8681-11-2021 Published online: 20 May 2022

Abstract

We study general spectral multiplier theorems for nonnegative self-adjoint operators on spaces of homogeneous type. We show that a Hörmander type spectral multiplier theorem follows from sub-Gaussian upper bounds for the corresponding heat kernel. Our result can be applied to fractal manifolds and quantum graphs.

Authors

  • Peng ChenDepartment of Mathematics
    Sun Yat-sen University
    Guangzhou, 510275, P.R. China
    e-mail
  • Xixi LinDepartment of Mathematics
    Sun Yat-sen University
    Guangzhou, 510275, P.R. China
    e-mail

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