Heat kernel upper bounds for symmetric Markov semigroups

2020/10/12 by Zhen-Qing Chen, Panki Kim, Chen, Zhen-Qing +5 · 2 citations
Mathematics · #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2010.05414

openalex publication_date 2020/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is well known that Nash-type inequalities for symmetric Dirichlet forms are equivalent to on-diagonal heat kernel upper bounds for the associated symmetric Markov semigroups. In this paper, we show that both imply (and hence are equivalent to) off-diagonal heat kernel upper bounds under some mild assumptions. Our approach is based on a new generalized Davies' method. Our results extend that of \citeCKS for Nash-type inequalities with power order considerably and also extend that of \citeGri for second order differential operators on a complete non-compact manifold.

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