Kato class measures of symmetric Markov processes under heat kernel estimates
Kato class measures of symmetric Markov processes under heat kernel estimates
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DOI：
10.1016/j.jfa.2006.10.010
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发表时间：
2007-09
影响因子：
1.7
通讯作者：
K. Kuwae;Masayuki Takahashi
中科院分区：
文献类型：
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作者：
K. Kuwae;Masayuki Takahashi
在允许热核上估计和下估计的对称马尔可夫过程框架下，我们建立了两类Kato类测度在温和条件下的一致性。一类加藤测度是由热核定义的，另一类是由格林核定义的，这取决于与热核估计相关的一些指数。我们还证明了在相同条件下，如果p大于与估计相关的常数，则半径为1且其范数相对于中心均匀的球上的第p个可积函数是Kato类。这是艾森曼和西蒙关于欧几里得空间上布朗运动的一些结果的完全推广。我们的结果可以应用于许多例子，例如对称（相对论）稳定过程、d集上的跳跃过程、黎曼流形上的布朗运动、分形上的扩散等等。
We establish the coincidence of two classes of Kato class measures in the framework of symmetric Markov processes admitting upper and lower estimates of heat kernel under mild conditions. One class of Kato class measures is defined by way of the heat kernel, another is defined in terms of the Green kernel depending on some exponents related to the heat kernel estimates. We also prove that pth integrable functions on balls with radius 1 having a uniformity of its norm with respect to centers are of Kato class if p is greater than a constant related to the estimate under the same conditions. These are complete extensions of some results for the Brownian motion on Euclidean space by Aizenman and Simon. Our result can be applicable to many examples, for instance, symmetric (relativistic) stable processes, jump processes on d-sets, Brownian motions on Riemannian manifolds, diffusions on fractals and so on.