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arXiv · 2306.08098

Hardy and Sobolev inequalities on antisymmetric functions

Thomas Hoffmann-Ostenhof·Ari Laptev·Il'ya Shcherbakov
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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.

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Thomas Hoffmann-Ostenhof, Ari Laptev, Il'ya Shcherbakov. 2023-06-13. Hardy and Sobolev inequalities on antisymmetric functions. https://arxiv.org/abs/2306.08098

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