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Off-diagonal upper estimates for the heat kernel of the Dirichlet forms on metric spaces

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Abstract

We give equivalent characterizations for off-diagonal upper bounds of the heat kernel of a regular Dirichlet form on the metric measure space, in two settings: for the upper bounds with the polynomial tail (typical for jump processes) and for the upper bounds with the exponential tail (for diffusions). Our proofs are purely analytic and do not use the associated Hunt process.

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Authors and Affiliations

  1. Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501, Bielefeld, Germany

    Alexander Grigor’yan

  2. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, P.R. China

    Jiaxin Hu

Authors
  1. Alexander Grigor’yan
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  2. Jiaxin Hu
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Correspondence to Jiaxin Hu.

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Grigor’yan, A., Hu, J. Off-diagonal upper estimates for the heat kernel of the Dirichlet forms on metric spaces. Invent. math. 174, 81–126 (2008). https://doi.org/10.1007/s00222-008-0135-9

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  • DOI: https://doi.org/10.1007/s00222-008-0135-9

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