Poincare-type inequalities for singular stable-like Dirichlet forms

[摘要] 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 a-stable process, and whose Levy jump kernel measure is concentrated on the union of the coordinate axes. Explicit and sharp criteria for Poincare inequality, super Poincare inequality and weak Poincare 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. (C) 2015 Elsevier Inc. All rights reserved.

[发布日期] 2015-12-15

[关键词] Singular stable-like non-local;Dirichlet form;(Super/weak) Poincare inequality;Entropy inequality;Tensorisation property;Lyapunov type conditions