The Davies method revisited for heat kernel upper bounds of regular Dirichlet forms on metric measure spaces

2016/05/18 by Jiaxin Hu, Hu, Jiaxin, Xuliang Li +1 · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #Analytic and geometric function theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1605.05548

openalex publication_date 2016/05/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We apply the Davies method to prove that for any regular Dirichlet form on a metric measure space, an off-diagonal stable-type upper bound of the heat kernel is equivalent to the conjunction of the on-diagonal upper bound, a cutoff inequality on any two concentric balls, and the jump kernel upper bound, for any walk dimension. If in addition the jump kernel vanishes, that is, if the Dirichlet form is strongly local, we obtain sub-Gaussian upper bound. This gives a unified approach to obtaining heat kernel upper bounds for both the non-local and the local Dirichlet forms.

Citations

• Transition Probabilities for Symmetric Jump Processes
• Brownian Motion and Harmonic Analysis on Sierpinski Carpets

Cited by

• Spectral bounds and heat kernel upper estimates for Dirichlet forms

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