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arXiv · 2010.05414

Heat kernel upper bounds for symmetric Markov semigroups

Zhen-Qing Chen·Panki Kim·Takashi Kumagai·Jian Wang
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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 \cite{CKS} for Nash-type inequalities with power order considerably and also extend that of \cite{Gri} for second order differential operators on a complete non-compact manifold.

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Zhen-Qing Chen, Panki Kim, Takashi Kumagai, Jian Wang. 2020-10-12. Heat kernel upper bounds for symmetric Markov semigroups. https://arxiv.org/abs/2010.05414

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