{"paper":{"title":"An optimal fractional Hardy inequality on the discrete half-line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CA","math.FA","math.MP","math.SP"],"primary_cat":"math.AP","authors_text":"Rub\\'en de la Fuente-Fern\\'andez, Ujjal Das","submitted_at":"2025-07-09T10:13:59Z","abstract_excerpt":"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 applic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.06716","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.06716/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}