(untitled) (Analysis in Theory and Applications, 2022)
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 Δ_G is defined by Δ_G= -^n_1_j=1 X^2_j. The operator defined by Δ_G-^n_1_j=1X_jppX_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.