Gaussian BV Functions and Gaussian BV Capacity on Stratified Groups (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 $$Δ_G= -\sum^{n_1}_{j=1} X^2_j. $$ The operator defined by $$Δ_G-\sum^{n_1}_{j=1}\frac{X_jp}{p}X_j$$ 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.
Keywords: Gaussian $p$ bounded variation; capacity; perimeter; stratified Lie group.