Optimal heat kernel bounds and asymptotics on Damek--Ricci spaces

2022/10/05 by Tommaso Bruno, Bruno, Tommaso, Federico Santagati +1
Mathematics · #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Advanced Harmonic Analysis Research

paper · pdf · doi:10.48550/arxiv.2210.02066

Abstract

We give optimal bounds for the radial, space and time derivatives of arbitrary order of the heat kernel of the Laplace--Beltrami operator on Damek--Ricci spaces. In the case of symmetric spaces of rank one, these complete and actually improve conjectured estimates by Anker and Ji. We also provide asymptotics at infinity of all the radial and time derivates of the kernel. Along the way, we provide sharp bounds for all the derivatives of the Riemannian distance and obtain analogous bounds for those of the heat kernel of the distinguished Laplacian.

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