@article{Mu2025, 
author = {Zimiao Mu and Feng Zhou},
title = {Kelvin transform on the Heisenberg group revisited and applications to the best constant of Hardy-Sobolev type inequality},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {8},
pages = {19438-19459},
keywords = {Heisenberg group, Kelvin transform, sub-Laplacian, Hardy-Sobolev type inequality, Best constant},
url = {https://www.sciopen.com/article/10.3934/math.2025868},
doi = {10.3934/math.2025868},
abstract = {In this paper we study the inversion map and the Kelvin transform on the Heisenberg group              H              n      . We first analyze the invariance of the Kelvin transform and provide an algebraic proof to the formula involving the sub-Laplacian. Furthermore, we apply the formula to seek the cylindrically symmetric solution to a sub-elliptic equation on              H              n       and determine the best constant of the Hardy-Sobolev type inequality.}
}