Given 0 < s < d/2 with s ≤ 1, we are interested in the large N-behavior of the optimal constant κN in the Hardy inequality ΣNn=1(-Δn)s ≥ κN Σn<m |Xn - Xm|-2s, when restricted to antisymmetric functions. We show that N1-2s/d κN has a positive, finite limit given by a certain variational problem, thereby generalizing a result of Lieb and Yau related to the Chandrasekhar theory of gravitational collapse.
No takes yet. Share an insight, caveat, or question.
Frank et al. (2024) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: