{"paper":{"title":"Optimal stability of Hardy-Littlewood-Sobolev and Sobolev inequalities of arbitrary orders with dimension-dependent constants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Guozhen Lu, Hanli Tang, Lu Chen","submitted_at":"2024-05-28T00:55:37Z","abstract_excerpt":"Recently, Dolbeault-Esteban-Figalli-Frank-Loss [20] established the optimal stability of the first-order $L^2$-Sobolev inequality with dimension-dependent constant. Subsequently, Chen-Lu-Tang [18] obtained the optimal stability for the $L^2$ fractional Sobolev inequality of order $s$ when $0<s<1$.This paper considers the remaining case $1<s<\\frac{n}{2}$. Our strategy is to first establish the optimal stability for the HLS inequality directly without using the stability of the Sobolev inequality. The main difficulty lies in establishing the optimal local stability of HLS inequality when $1<s<\\f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.17727","kind":"arxiv","version":3},"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/2405.17727/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"}