Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4614691 | Journal of Mathematical Analysis and Applications | 2015 | 26 Pages |
Abstract
This paper is concerned with a class of singular stable-like Dirichlet forms on RdRd, 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 RdRd, 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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Jian Wang,