Poincar\'e-type Inequalities for Singular Stable-Like Dirichlet Forms
Poincar\'e-type Inequalities for Singular Stable-Like Dirichlet Forms
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DOI：
10.1016/j.jmaa.2015.06.071
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发表时间：
2015-08
期刊：
影响因子：
--
通讯作者：
Jian Wang
中科院分区：
文献类型：
--
作者：
Jian Wang
本文讨论了一类由一维对称α-稳定过程的d个独立副本生成的Rd上的奇异类稳定Dirichlet型，它的Lévy跳核测度集中在坐标轴并集上.给出了这类奇异Dirichlet形式的Poincaré不等式、超Poincaré不等式和弱Poincaré不等式的显式且精确的判据。当参考测度是RD上的乘积测度时，我们还考虑了相应的Dirichlet形式的熵不等式，它类似于局部Dirichlet形式的Log-Soblev不等式，并且具有张量性。
This paper is concerned with a class of singular stable-like Dirichlet forms on R d, which are generated by d independent copies of a one-dimensional symmetric α-stable process, and whose Lévy jump kernel measure is concentrated on the union of the coordinate axes. Explicit and sharp criteria for Poincaré inequality, super Poincaré inequality and weak Poincaré inequality of such singular Dirichlet forms are presented. When the reference measure is a product measure on R d, we also consider the entropy inequality for the associated Dirichlet forms, which is similar to the log-Sobolev inequality for local Dirichlet forms, and enjoys the tensorisation property.