AN ANALYTICAL APPROACH TO HEAT KERNEL ESTIMATES ON STRONGLY RECURRENT METRIC SPACES
AN ANALYTICAL APPROACH TO HEAT KERNEL ESTIMATES ON STRONGLY RECURRENT METRIC SPACES
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DOI：
10.1017/s001309150500177x
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发表时间：
2008-02
影响因子：
0.7
通讯作者：
Jiaxin Hu
中科院分区：
文献类型：
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作者：
Jiaxin Hu
本文证明了在强常返紧度量空间上正则Dirichlet型热核的次高斯估计等价于测度的正则性、有效电阻的双边界和半群的局部性。有效电阻的上界蕴含了Dirichlet型域的紧嵌入定理，并给出了Dirichlet型域上具有零边界条件的绿色函数的存在性.绿色函数在我们的分析中起着重要的作用。我们在本文中的重点是推导双边次高斯边界的热核的分析方面。我们还给出了概率解释的每个主要的分析步骤。
Abstract In this paper we prove that sub-Gaussian estimates of heat kernels of regular Dirichlet forms are equivalent to the regularity of measures, two-sided bounds of effective resistances and the locality of semigroups, on strongly recurrent compact metric spaces. Upper bounds of effective resistances imply the compact embedding theorem for domains of Dirichlet forms, and give rise to the existence of Green functions with zero Dirichlet boundary conditions. Green functions play an important role in our analysis. Our emphasis in this paper is on the analytic aspects of deriving two-sided sub-Gaussian bounds of heat kernels. We also give the probabilistic interpretation for each of the main analytic steps.