{"paper":{"title":"Caffarelli-Kohn-Nirenberg type inequalities of fractional order with applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Boumediene Abdellaoui, Rachid Bentifour","submitted_at":"2016-11-15T07:36:36Z","abstract_excerpt":"Let $0<s<1$ and $p>1$ be such that $ps<N$. Assume that $\\Omega$ is a bounded domain containing the origin. Staring from the ground state inequality by R. Frank and R. Seiringer we obtain: 1- The following improved Hardy inequality for $p\\ge 2$ For all $q<p$, there exists a positive constant $C\\equiv C(\\Omega, q, N, s)$ such that\n  $$ \\int_{{\\mathbb R}^N}\\int_{{\\mathbb R}^N} \\, \\frac{|u(x)-u(y)|^{p}}{|x-y|^{N+ps}}\\,dx\\,dy - \\Lambda_{N,p,s} \\int_{{\\mathbb R}^N} \\frac{|u(x)|^p}{|x|^{p}}\\,dx\\geq C \\int_{\\Omega}\\dint_{\\Omega}\\frac{|u(x)-u(y)|^p}{|x-y|^{N+qs}}dxdy $$ for all $u \\in \\mathcal{C}_0^\\in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04724","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":""},"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"}