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Volume 37, Issue 3
Gaussian BV Functions and Gaussian BV Capacity on Stratified Groups

Jizheng Huang, Pengtao Li & Yu Liu

Anal. Theory Appl., 37 (2021), pp. 311-329.

Published online: 2021-09

[An open-access article; the PDF is free to any online user.]

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  • 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.

  • AMS Subject Headings

42B35, 47A60, 32U20, 22E30

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COPYRIGHT: © Global Science Press

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@Article{ATA-37-311, author = {Huang , JizhengLi , Pengtao and Liu , Yu}, title = {Gaussian BV Functions and Gaussian BV Capacity on Stratified Groups}, journal = {Analysis in Theory and Applications}, year = {2021}, volume = {37}, number = {3}, pages = {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.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2021.lu80.03}, url = {http://global-sci.org/intro/article_detail/ata/19877.html} }
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 -

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.

Huang , JizhengLi , Pengtao and Liu , Yu. (2021). Gaussian BV Functions and Gaussian BV Capacity on Stratified Groups. Analysis in Theory and Applications. 37 (3). 311-329. doi:10.4208/ata.2021.lu80.03
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