A survey of Hardy type inequalities on homogeneous groups
Abstract
In this review paper, we survey Hardy type inequalities from the point of view of Folland and Stein's homogeneous groups. Particular attention is paid to Hardy type inequalities on stratified groups which give a special class of homogeneous groups. In this environment, the theory of Hardy type inequalities becomes intricately intertwined with the properties of sub-Laplacians and more general subelliptic partial differential equations. Particularly, we discuss the Badiale-Tarantello conjecture and a conjecture on the geometric Hardy inequality in a half-space of the Heisenberg group with a sharp constant.
Cite
@article{arxiv.2005.03614,
title = {A survey of Hardy type inequalities on homogeneous groups},
author = {Durvudkhan Suragan},
journal= {arXiv preprint arXiv:2005.03614},
year = {2022}
}
Comments
20 pages, these are notes mainly from my lecture at the 12th ISAAC Congress in Aveiro (2019), updated version to appear in series of Springer Proceedings in Mathematics and Statistics