An optimal fractional Hardy inequality on the discrete half-line

2025/07/09 by Ujjal Das, Das, Ujjal, Rubén de la Fuente-Fernández +1 · 2 citations
Mathematics · #Nonlinear Partial Differential Equations #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems

paper · pdf · doi:10.48550/arxiv.2507.06716

Abstract

In the context of Hardy inequalities for the fractional Laplacian (-Δ_ℕ)^σ on the discrete half-line ℕ, we provide an optimal Hardy-weight W^op_σ for exponents σ∈(0,1]. As a consequence, we provide an estimate of the sharp constant in the fractional Hardy inequality with the classical Hardy-weight n^-2σ on ℕ. It turns out that for σ=1 the Hardy-weight W^op₁ is pointwise larger than the optimal Hardy-weight obtained by Keller--Pinchover--Pogorzelski near infinity. As an application of our main result, we obtain unique continuation results at infinity for the solutions of some fractional Schrödinger equation.

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