Hardy and Sobolev inequalities on antisymmetric functions

We obtain sharp Hardy inequalities on antisymmetric functions, where antisymmetry is understood for multi-dimensional particles. Partially it is an extension of the paper [Th. Hoffmann-Ostenhof and A. Laptev, Hardy inequalities with homogeneous weights, J. Funct. Anal. 268 (2015) 3278–3289], where H...

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Bibliographic Details
Published in:Bulletin of Mathematical Sciences
Main Authors: Th. Hoffmann-Ostenhof, A. Laptev, I. Shcherbakov
Format: Article in Journal/Newspaper
Language:English
Published: World Scientific Publishing 2024
Subjects:
Hardy inequalities
antisymmetric functions
Sobolev inequalities
Caffarelli–Kohn–Nirenberg inequality
Mathematics
QA1-939
laptev
Online Access:https://doi.org/10.1142/S1664360723500108
https://doaj.org/article/4a5cfff9950b40438cfe37b170ea8168
Description
Summary:We obtain sharp Hardy inequalities on antisymmetric functions, where antisymmetry is understood for multi-dimensional particles. Partially it is an extension of the paper [Th. Hoffmann-Ostenhof and A. Laptev, Hardy inequalities with homogeneous weights, J. Funct. Anal. 268 (2015) 3278–3289], 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 Schrödinger operators.

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