Li--Yau Inequalities for Dunkl Heat Equations

Abstract

Motivated by recent works due to Yu-Zhao [J. Geom. Anal. 2020] and Weber-Zacher [arXiv:2012.12974], we study Li-Yau inequalities for the heat equation corresponding to the Dunkl Laplacian, which is a non-local operator parameterized by reflection groups and multiplicity functions. The results are sharp in the particular case when the reflection group is isometric to Z d 2 .