{"paper":{"title":"Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Avas Banerjee, Debdip Ganguly, Vivek Sahu","submitted_at":"2026-05-15T09:06:31Z","abstract_excerpt":"A classical result due to Frank and Seiringer asserts that for $1\\leq p<\\frac Ns$, there exists a sharp constant $\\mathcal{C}_{N,s,p}>0$ such that $$ \\delta_{s,p}(u):=\\int_{\\mathbb{R}^N}\\int_{\\mathbb{R}^N}\\frac{|u(x)-u(y)|^p}{|x-y|^{N+sp}}\\,dx\\,dy-\\mathcal{C}_{N,s,p}\\int_{\\mathbb{R}^N}\\frac{|u(x)|^p}{|x|^{sp}}\\,dx\\ge0, $$ for all $u\\in W^{s,p}(\\mathbb{R}^N)$. The optimal constant is explicitly known. We investigate quantitative refinements of this inequality. Our first result shows that, under the normalization $ \\int_{\\mathbb{R}^N}\\frac{|u(x)|^p}{|x|^{sp}}\\,dx=1,$ the inequality \\[ \\delta_{s,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.15748","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/2605.15748/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-19T17:33:48.771126Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T17:21:55.971640Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"44568f5733a1210c2e9d4458c7931f395ab2db84ccc613fbf79548d74403c5a1"},"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"}