论文标题
$ l^p $ -green-tight量的$ l^p $ -kato类的对称马尔可夫流程
$L^p$-Green-tight measures of $L^p$-Kato class for symmetric Markov processes
论文作者
论文摘要
在本文中，我们介绍了$ l^p $ - 格林至关重要的指标，$ l^p $ -kato类在对称马尔可夫流程的框架中。 $ l^p $ - 绿色密度的$ l^p $ -kato类的措施由$ p $ - 分辨率内核的功率定义。我们首先证明，在$ l^p $ - 格林的紧密度下，将扩展的dirichlet空间嵌入$ l^{2p}（e;μ）$在瞬态马尔可夫流程的绝对连续性下是紧凑的，这是Takeeda最近开创性工作的扩展。其次，我们证明了两类$ l^p $ - 绿色紧密度之间的巧合，一个最初是由Zhao引入的，另一个是由Chen发明的。最后，我们证明，我们的$ l^p $ - 格林至关重要的款项$ l^p $ -kato类班级与$ l^p $ - 绿色级别的班级相吻合 - 根据全球热核心估计，绿色内核的绿色内核级别。我们将结果应用于$ d $ d $ dimensional andRotation andRotationally ontrotration symmetric symmetric $α$ - 稳定的流程上的$ \ mathbb {r}^d $。
In this paper, we introduce the notion of $L^p$-Green-tight measures of $L^p$-Kato class in the framework of symmetric Markov processes. The class of $L^p$-Green-tight measures of $L^p$-Kato class is defined by the $p$-th power of resolvent kernels. We first prove that under the $L^p$-Green tightness of the measure $μ$, the embedding of extended Dirichlet space into $L^{2p}(E;μ)$ is compact under the absolute continuity condition for transient Markov processes, which is an extension of recent seminal work by Takeda. Secondly, we prove the coincidence between two classes of $L^p$-Green-tightness, one is originally introduced by Zhao, and another one is invented by Chen. Finally, we prove that our class of $L^p$-Green-tight measures of $L^p$-Kato class coincides with the class of $L^p$-Green tight measures of Kato class in terms of Green kernel under the global heat kernel estimates. We apply our results to $d$-dimensional Brownian motion androtationally symmetric relativistic $α$-stable processes on $\mathbb{R}^d$.
