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arXiv · 2306.00531

Hardy inequalities for antisymmetric functions

Shubham Gupta
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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.

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Shubham Gupta. 2023-06-01. Hardy inequalities for antisymmetric functions. https://doi.org/10.1016/j.na.2024.113619

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