Hardy inequalities for antisymmetric functions

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.

Minor changes

References in corpus (4)

• A sharp form of the discrete Hardy inequality and the Keller-Pinchover-Pogorzelski inequality
• An improved discrete Rellich inequality on the half-line
• Hardy and Rellich inequality on lattices
• One dimensional sharp discrete Hardy-Rellich inequalities