For σ in (0,1], the paper constructs an explicit optimal Hardy weight W^op_σ for (-Δ_N)^σ, with W^op_σ(n) approximately n^{-2σ} and an upper bound C_σ for the best constant in the n^{-2σ} Hardy inequality.
Optimal Hardy inequalities for Schrödinger operators on graphs.Comm
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An optimal fractional Hardy inequality on the discrete half-line
For σ in (0,1], the paper constructs an explicit optimal Hardy weight W^op_σ for (-Δ_N)^σ, with W^op_σ(n) approximately n^{-2σ} and an upper bound C_σ for the best constant in the n^{-2σ} Hardy inequality.