Li--Yau Inequalities for Dunkl Heat Equations

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 ${\mathbb{Z}}_2^d$.