Parabolic mean value inequality and on-diagonal upper bound of the heat kernel on doubling spaces

Alexander Grigor'yan University of Bielefeld, Germany Eryan Hu Tianjin University, China Jiaxin Hu Tsinghua University, China

Geometric Analysis and Geometric Topology mathscidoc:2212.15001

2022.12
We prove the diagonal upper bound of heat kernels for regular Dirichlet forms on metric measure spaces with volume doubling condition. As hypotheses, we use the Faber-Krahn inequality, the generalized capacity condition and an upper bound for the integrated tail of the jump kernel. The proof goes though a parabolic mean value inequality for subcaloric functions.
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@inproceedings{alexander2022parabolic,
  title={Parabolic mean value inequality and on-diagonal upper bound of the heat kernel on doubling spaces},
  author={Alexander Grigor'yan, Eryan Hu, and Jiaxin Hu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20221206090203540032740},
  year={2022},
}
Alexander Grigor'yan, Eryan Hu, and Jiaxin Hu. Parabolic mean value inequality and on-diagonal upper bound of the heat kernel on doubling spaces. 2022. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20221206090203540032740.
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