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More precisely, we improve the Poincar\\'e inequality associated with the above ratio by showing the existence of $k$ Hardy-type remainde"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1511.00474","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-11-02T12:46:38Z","cross_cats_sorted":[],"title_canon_sha256":"2bcff5aa021e1ffb0f5fe7c858d1260e3e80d76c80990b96cb5bff16e1941537","abstract_canon_sha256":"d196c351274b1e3d719e55ef28ae3ea0e68bf8ee373602d1859b512a19030e15"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:12.230684Z","signature_b64":"RC/V4aOpQ4hn6z+kNjcB5p4avBgbx5k96vWhEAoUmppatc9SMNe13SC7/1ACf4tiOKBZrPjPXclhulKGCaICBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8ed9ce0a9b895539e8faf6de2a3acadcf8d037e54d52356fb0b3bc1b26bb93f3","last_reissued_at":"2026-05-18T01:28:12.229997Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:12.229997Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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