{"paper":{"title":"Remainder terms, profile decomposition and sharp quantitative stability in the fractional nonlocal Sobolev-type inequality with $n>2s$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Minbo Yang, Qikai Lu, Shunneng Zhao","submitted_at":"2025-03-09T14:31:17Z","abstract_excerpt":"In this paper, we study the following fractional nonlocal Sobolev-type inequality\n  \\begin{equation*}\n  C_{HLS}\\bigg(\\int_{\\mathbb{R}^n}\\big(|x|^{-\\mu} \\ast |u|^{p_s}\\big)|u|^{p_s} dx\\bigg)^{\\frac{1}{p_s}}\\leq\\|u\\|_{\\dot{H}^s(\\mathbb{R}^n)}^2\\quad \\mbox{for all}~~u\\in \\dot{H}^s(\\mathbb{R}^n),\n  \\end{equation*}\n  induced by the classical fractional Sobolev inequality and Hardy-Littlewood-Sobolev inequality for $s\\in(0,\\frac{n}{2})$, $\\mu\\in(0,n)$ and where $p_{s}=\\frac{2n-\\mu}{n-2s}\\geq2$ is energy-critical exponent. The $C_{HLS}>0$ is a constant depending on the dimension $n$, parameters $s$ a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.06636","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/2503.06636/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"}