Harnack inequality for stable processes on d-sets
Harnack inequality for stable processes on d-sets
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DOI：
10.4064/sm158-2-5
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发表时间：
2003
影响因子：
0.8
通讯作者：
K. Bogdan;A. Stos;Paweł Sztonyk
中科院分区：
文献类型：
--
作者：
K. Bogdan;A. Stos;Paweł Sztonyk
我们研究函数的性质，这些函数是关于d-集上的稳定过程的调和函数，例如Sierpi«ski垫片或地毯。证明了这类函数的Harnack不等式。对于每一个过程，我们估计它的过渡密度和球的调和测度。证明了调和测度的密度连续性。我们还给出了d-集的正则子集上调和函数的衰减率的一些结果。在Sierpi«ski垫片的情况下，我们甚至得到边界Harnack原理。
We investigate properties of functions which are harmonic with respect to -stable processes on d-sets such as the Sierpi«ski gasket or carpet. We prove the Harnack inequality for such functions. For every process we estimate its transition density and harmonic measure of the ball. We prove continuity of the density of the harmonic measure. We also give some results on the decay rate of harmonic functions on regular subsets of the d-set. In the case of the Sierpi«ski gasket we even obtain the Boundary Harnack Principle.