Spectral multiplier theorem and sub-Gaussian heat kernel estimates
Volume 170 / 2022
Colloquium Mathematicum 170 (2022), 193-210
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.
