An optimal fractional Hardy inequality on the discrete half-line
In the context of Hardy inequalities for the fractional Laplacian $(-\Delta_{\mathbb{N}})^{\sigma}$ on the discrete half-line $\mathbb{N}$, we provide an optimal Hardy-weight $W^{\mathrm{op}}_{\sigma}$ for exponents $\sigma\in\left(0,1\right]$. As a consequence, we provide an estimate of the sharp c...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2026 |
| País: | España |
| Institución: | Basque Center for Applied Mathematics (BCAM) |
| Repositorio: | BIRD. BCAM's Institutional Repository Data |
| OAI Identifier: | oai:bird.bcamath.org:20.500.11824/2155 |
| Acceso en línea: | http://hdl.handle.net/20.500.11824/2155 https://doi.org/10.1007/s00526-025-03217-w |
| Access Level: | acceso abierto |
| Palabra clave: | Hardy inequality, fractional powers, discrete Laplacian, criticality, subcriticality, optimal weight, ground state representation |
| Sumario: | In the context of Hardy inequalities for the fractional Laplacian $(-\Delta_{\mathbb{N}})^{\sigma}$ on the discrete half-line $\mathbb{N}$, we provide an optimal Hardy-weight $W^{\mathrm{op}}_{\sigma}$ for exponents $\sigma\in\left(0,1\right]$. As a consequence, we provide an estimate of the sharp constant in the fractional Hardy inequality with the classical Hardy-weight $n^{-2\sigma}$ on $\mathbb{N}$. It turns out that for $\sigma =1$ the Hardy-weight $W^{\mathrm{op}}_{1}$ 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 Schr\"odinger equation. |
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