Given 0<s< d2 with s≤ 1, we are interested in the large N-behavior of the optimal constant κN in the Hardy inequality ∑ₙ₌₁N (-Δₙ)ˢ ≥ κN ∑n<m |Xₙ-Xₘ|⁻²ˢ, when restricted to antisymmetric functions. We show that N^1-2sdκN 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.
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Frank et al. (2024) studied this question.
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