Abstract In the context of Hardy inequalities for the fractional Laplacian (- ₍) ^ (- Δ N) σ on the discrete half-line N N, we provide an optimal Hardy-weight W^op W σ op for exponents (0, 1] 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^-2 n - 2 σ on N N. It turns out that for =1 σ = 1 the Hardy-weight W^op₁ W 1 op 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.
Das et al. (Mon,) studied this question.