Gaussian BV Functions and Gaussian BV Capacity on Stratified Groups

Let G be a stratified Lie group and let{X_(1)……,X_(n1)}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 Xjp/pXj 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.