{"paper":{"title":"Improved higher order Poincar\\'e inequalities on the hyperbolic space via Hardy-type remainder terms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Debdip Ganguly, Elvise Berchio","submitted_at":"2015-11-02T12:46:38Z","abstract_excerpt":"The paper deals about Hardy-type inequalities associated with the following higher order Poincar\\'e inequality:\n  $$\n  \\left( \\frac{N-1}{2} \\right)^{2(k -l)} := \\inf_{ u \\in C_{c}^{\\infty} \\setminus \\{0\\}} \\frac{\\int_{\\mathbb{H}^{N}} |\\nabla_{\\mathbb{H}^{N}}^{k} u|^2 \\ dv_{\\mathbb{H}^{N}}}{\\int_{\\mathbb{H}^{N}} |\\nabla_{\\mathbb{H}^{N}}^{l} u|^2 \\ dv_{\\mathbb{H}^{N}} }\\,,\n  $$ where $0 \\leq l < k$ are integers and $\\mathbb{H}^{N}$ denotes the hyperbolic space. More precisely, we improve the Poincar\\'e inequality associated with the above ratio by showing the existence of $k$ Hardy-type remainde"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.00474","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"}