An optimal fractional Hardy inequality on the discrete half-line
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911047263191040 |
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| author | Das, Ujjal de la Fuente-Fernández, Rubén |
| author_facet | Das, Ujjal de la Fuente-Fernández, Rubén |
| contents | In the context of Hardy inequalities for the fractional Laplacian $(-Δ_{\mathbb{N}})^σ$ on the discrete half-line $\mathbb{N}$, we provide an optimal Hardy-weight $W^{\mathrm{op}}_σ$ for exponents $σ\in\left(0,1\right]$. As a consequence, we provide an estimate of the sharp constant in the fractional Hardy inequality with the classical Hardy-weight $n^{-2σ}$ on $\mathbb{N}$. It turns out that for $σ=1$ 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 Schrödinger equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06716 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An optimal fractional Hardy inequality on the discrete half-line Das, Ujjal de la Fuente-Fernández, Rubén Analysis of PDEs Mathematical Physics Classical Analysis and ODEs Functional Analysis Spectral Theory In the context of Hardy inequalities for the fractional Laplacian $(-Δ_{\mathbb{N}})^σ$ on the discrete half-line $\mathbb{N}$, we provide an optimal Hardy-weight $W^{\mathrm{op}}_σ$ for exponents $σ\in\left(0,1\right]$. As a consequence, we provide an estimate of the sharp constant in the fractional Hardy inequality with the classical Hardy-weight $n^{-2σ}$ on $\mathbb{N}$. It turns out that for $σ=1$ 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 Schrödinger equation. |
| title | An optimal fractional Hardy inequality on the discrete half-line |
| topic | Analysis of PDEs Mathematical Physics Classical Analysis and ODEs Functional Analysis Spectral Theory |
| url | https://arxiv.org/abs/2507.06716 |