Gaussian BV Functions and Gaussian BV Capacity on Stratified Groups

Abstract

. Let G be a stratified Lie group and let { X 1 , · · · , X n 1 } be a basis of the first layer of the Lie algebra of G . The sub-Laplacian ∆ G is defined by ∆ G = − n 1 ∑ j = 1 X 2 j . The operator defined by ∆ G − n 1 ∑ j = 1 X j p p X j is called the Ornstein-Uhlenbeck operator on G , where p is a heat kernel at time 1 on G . In this paper, we investigate Gaussian BV functions and Gaussian BV capacities associated with the Ornstein-Uhlenbeck operator on the stratified Lie group