Hardy and Sobolev inequalities on antisymmetric functions
Analysis of PDEs
2023-06-16 v1 Functional Analysis
Abstract
We obtain sharp Hardy inequalities on antisymmetric functions where antisymmetry is understood for multi-dimensional particles. Partially it is an extension of the previously published paper \cite{HL}, where Hardy's inequalities were considered for the antisymmetric functions in the case of the 1D particles. As a byproduct we obtain some Sobolev and Gagliardo-Nirenberg type inequalities that are applied to the study of spectral properties of Schr\"odinger operators.
Cite
@article{arxiv.2306.08098,
title = {Hardy and Sobolev inequalities on antisymmetric functions},
author = {Thomas Hoffmann-Ostenhof and Ari Laptev and Il'ya Shcherbakov},
journal= {arXiv preprint arXiv:2306.08098},
year = {2023}
}
Comments
19 pages, 1 figure