TY - JOUR
T1 - Gaussian BV Functions and Gaussian BV Capacity on Stratified Groups
AU - Huang , Jizheng
AU - Li , Pengtao
AU - Liu , Yu
JO - Analysis in Theory and Applications
VL - 3
SP - 311
EP - 329
PY - 2021
DA - 2021/09
SN - 37
DO - http://doi.org/10.4208/ata.2021.lu80.03
UR - https://global-sci.org/intro/article_detail/ata/19877.html
KW - Gaussian $p$ bounded variation, capacity, perimeter, stratified Lie group.
AB - <p style="text-align: justify;">Let $G$ be a stratified Lie group and let $\{X_1, \cdots, X_{n_1}\}$ be a basis of the first layer of the Lie algebra of $G$. The sub-Laplacian $\Delta_G$ is defined by $$\Delta_G= -\sum^{n_1}_{j=1} X^2_j. $$ The operator defined by $$\Delta_G-\sum^{n_1}_{j=1}\frac{X_jp}{p}X_j$$ 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.</p>