{"paper":{"title":"Sharp Hardy-Adams inequalities for bi-Laplacian on hyperbolic space of dimension four","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Guozhen Lu, Qiaohua Yang","submitted_at":"2017-03-23T17:27:40Z","abstract_excerpt":"We establish sharp Hardy-Adams inequalities on hyperbolic space $\\mathbb{B}^{4}$ of dimension four. Namely, we will show that for any $\\alpha>0$ there exists a constant $C_{\\alpha}>0$ such that \\[ \\int_{\\mathbb{B}^{4}}(e^{32\\pi^{2} u^{2}}-1-32\\pi^{2} u^{2})dV=16\\int_{\\mathbb{B}^{4}}\\frac{e^{32\\pi^{2} u^{2}}-1-32\\pi^{2} u^{2}}{(1-|x|^{2})^{4}}dx\\leq C_{\\alpha}. \\] for any $u\\in C^{\\infty}_{0}(\\mathbb{B}^{4})$ with \\[ \\int_{\\mathbb{B}^{4}}\\left(-\\Delta_{\\mathbb{H}}-\\frac{9}{4}\\right)(-\\Delta_{\\mathbb{H}}+\\alpha)u\\cdot udV\\leq1. \\]\n  As applications, we obtain a sharpened Adams inequality on hype"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.08149","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":""},"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"}