Heat kernel estimates for jump processes of mixed types on metric measure spaces
Heat kernel estimates for jump processes of mixed types on metric measure spaces
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DOI：
10.1007/s00440-007-0070-5
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发表时间：
2007-04
影响因子：
2
通讯作者：
Zhen-Qing Chen;T. Kumagai
中科院分区：
文献类型：
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作者：
Zhen-Qing Chen;T. Kumagai
在本文中，我们研究了一类度量测度空间上的对称跳跃型过程，其跳跃强度与空间上的径向对称函数相当。度量测度空间类包括 Alforsd 正则集，它是一类包含几何自相似集的分形集。我们的跳跃型过程的一个典型例子是具有跳跃强度的对称跳跃过程，其中ν是概率测度，c(α,x,y)是在(x,y)上对称且在两个正常数之间有界的联合可测函数，c0(x,y)是在(x,y)上对称且在γ1和γ2之间有界的联合可测函数，其中 γ2≥ γ1> 0 或 γ1=γ2= 0。此示例包含混合对称稳定过程 on 以及混合相对论对称稳定过程 on。我们建立了抛物线 Harnack 原理，并针对这种跳跃型过程导出了尖锐的两侧热核估计。
In this paper, we investigate symmetric jump-type processes on a class of metric measure spaces with jumping intensities comparable to radially symmetric functions on the spaces. The class of metric measure spaces includes the Alforsd-regular sets, which is a class of fractal sets that contains geometrically self-similar sets. A typical example of our jump-type processes is the symmetric jump process with jumping intensitywhere ν is a probability measure on,c(α,x,y) is a jointly measurable function that is symmetric in (x,y) and is bounded between two positive constants, andc0(x,y) is a jointly measurable function that is symmetric in (x,y) and is bounded between γ1and γ2, where either γ2≥ γ1> 0 or γ1= γ2= 0. This example contains mixed symmetric stable processes onas well as mixed relativistic symmetric stable processes on. We establish parabolic Harnack principle and derive sharp two-sided heat kernel estimate for such jump-type processes.