On a theorem of Grigor'yan, Hu and Lau

TL;DR

This paper refines a theorem by Grigor'yan, Hu, and Lau to establish a precise moment condition on the heat kernel that determines when a family of Besov spaces related to Dirichlet energy becomes trivial, deepening understanding of heat kernel behavior.

Contribution

It provides a sharper criterion linking heat kernel moments to the triviality threshold of associated Besov spaces, extending previous results.

Findings

Identifies a specific moment condition on the heat kernel

Characterizes the critical exponent for Besov space triviality

Enhances understanding of heat kernel and function space relationships

Abstract

We refine a result of Grigor'yan, Hu and Lau to give a moment condition on a heat kernel which characterizes the critical exponent at which a family of Besov spaces associated to the Dirichlet energy becomes trivial.