Hardy inequalities for antisymmetric functions
Functional Analysis
2024-08-14 v2 Mathematical Physics
math.MP
Spectral Theory
Abstract
We study Hardy inequalities for antisymmetric functions in three different settings: euclidean space, torus and the integer lattice. In particular, we show that under the antisymmetric condition the sharp constant in Hardy inequality increases substantially and grows as d^4 as d \rightarrow \infty in all cases. As a side product, we prove Hardy inequality on a domain whose boundary forms a corner at the point of singularity x=0.
Cite
@article{arxiv.2306.00531,
title = {Hardy inequalities for antisymmetric functions},
author = {Shubham Gupta},
journal= {arXiv preprint arXiv:2306.00531},
year = {2024}
}
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