论文标题
对称跳跃过程的稳定性结果在公制测量空间上具有原子。长版
Stability results for symmetric jump processes on metric measure spaces with atoms. Long version
论文作者
论文摘要
考虑一个对称的Markovian跳跃过程$ \ {x_t \} $在公制度量空间$（m，d，μ）$上。 Chen，Kumagai和Wang最近显示，假设$（m，d，μ）$满足体积加倍和反向数量加倍条件，那么在跳跃措施的有限扰动下，双面热核估计值和抛物线harnack不平等都稳定。如果$（m，d，μ）$是图形（或更一般的，如果$ m $包含任何原子$ x $，则这些结果不适用，因此$μ（x）> 0 $），因为反向体积加倍无法在原子上保持空间是不可能的。我们将Chen，Kumagai和Wang的结果推广到较大类别的度量度量空间，包括所有无限图，体积加倍。我们的主要工具是构造“辅助空间”，该空间使原子平滑。我们表明，许多属性从$（M，D，μ）$转移到辅助空间，反之亦然，包括热核估计值，抛物线抛物性harnack不平等及其稳定的特征。
Consider a symmetric Markovian jump process $\{X_t\}$ on a metric measure space $(M, d, μ)$. Chen, Kumagai, and Wang recently showed that two-sided heat kernel estimates and the parabolic Harnack inequality are both stable under bounded perturbations of the jumping measure, assuming $(M, d, μ)$ satisfies the volume-doubling and reverse-volume-doubling conditions. These results do not apply if $(M, d, μ)$ is a graph (or more generally, if $M$ contains any atoms $x$ such that $μ(x)>0$) because it is impossible for reverse-volume-doubling to hold on a space with atoms. We generalize the results of Chen, Kumagai, and Wang to a larger class of metric measure spaces, including all infinite graphs with volume-doubling. Our main tool is the construction of an "auxiliary space" that smooths out the atoms. We show that many properties transfer from $(M, d, μ)$ to the auxiliary space, and vice versa, including heat kernel estimates, the parabolic Harnack inequality, and their stable characterizations.
