On the compactness of the (non)radial Sobolev spaces
Functional Analysis
2022-06-29 v1 Analysis of PDEs
Abstract
In this note, we give the affirmative answer of the question in [18], which is a compactness result of the non-radial Sobolev spaces. As an application, we show the existence of an extremal function of the critical Hardy inequality under spherical average zero. Next, we give an improvement of the compactness results of the radial Sobolev spaces in [8]. In Appendix, we give an alternative proof of Hardy type inequalities under spherical average zero.
Cite
@article{arxiv.2206.13775,
title = {On the compactness of the (non)radial Sobolev spaces},
author = {Shuji Machihara and Megumi Sano},
journal= {arXiv preprint arXiv:2206.13775},
year = {2022}
}
Comments
20 pages