热核的非对角下限估计和荷尔德正则性

IF 0.5 4区数学 Q3 MATHEMATICS Asian Journal of Mathematics Pub Date : 2024-07-12 DOI:10.4310/ajm.2023.v27.n5.a3

Alexander Grigor’yan, Eryan Hu, Jiaxin Hu

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摘要

我们研究了具有加倍度量的度量空间上正则对称德里赫特形式的热核，特别是跃迁度量的性质与热核的长期行为之间的联系。在适当的最优假设下，我们得到了热核的赫尔德正则性和下限估计值。

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Off-diagonal lower estimates and Hölder regularity of the heat kernel

We study the heat kernel of a regular symmetric Dirichlet form on a metric space with doubling measure, in particular, a connection between the properties of the jump measure and the long time behaviour of the heat kernel. Under appropriate optimal hypotheses, we obtain the Hölder regularity and lower estimates of the heat kernel.

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