{"paper":{"title":"Fractional Hardy inequalities on $C^{1,1}$ open sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Abdelrazek Dieb, Remi Yvant Temgoua","submitted_at":"2026-02-11T03:01:37Z","abstract_excerpt":"Let $\\Omega$ be a bounded open set of class $C^{1,1}$ in $\\mathbb{R}^N$ and $s\\in(\\frac{1}{2}, 1)$. We study a family of fractional Hardy-type inequalities \\begin{equation} \\frac{c_{N,s}}{2}\\displaystyle\\iint_{\\Omega\\times\\Omega}\\frac{(u(x)-u(y))^2}{|x-y|^{N+2s}}\\ dxdy-\\displaystyle\\lambda\\int_{\\Omega}u^2\\ dx\\geq C\\displaystyle\\int_{\\Omega}\\frac{u^2}{\\delta^{2s}}\\ dx,~~~\\quad\\forall\\lambda\\in\\mathbb{R},~~~~~~~(0.1) \\end{equation} with $u\\in C_c^\\infty(\\Omega)$ and $C=C(\\Omega,s,N,\\lambda)>0$. We show that the best constant in $(0.1)$ is achieved if and only if $\\lambda>\\lambda^*(s,\\Omega)$, fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.10463","kind":"arxiv","version":2},"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/2602.10463/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"}