Year: 2021
Author: Jizheng Huang, Pengtao Li, Yu Liu
Analysis in Theory and Applications, Vol. 37 (2021), Iss. 3 : pp. 311–329
Abstract
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.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.2021.lu80.03
Analysis in Theory and Applications, Vol. 37 (2021), Iss. 3 : pp. 311–329
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Gaussian $p$ bounded variation capacity perimeter stratified Lie group.
Author Details
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