{"paper":{"title":"Second order Sobolev type inequalities in the hyperbolic spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"Van Hoang Nguyen","submitted_at":"2018-05-05T13:18:00Z","abstract_excerpt":"We establish several Poincar\\'e--Sobolev type inequalities for the Lapalce--Beltrami operator $\\Delta_g$ in the hyperbolic space $\\mathbb H^n$ with $n\\geq 5$. These inequalities could be seen as the improved second order Poincar\\'e inequality with remainder terms involving with the sharp Rellich inequality or sharp Sobolev inequality in $\\mathbb H^n$. The novelty of these inequalities is that it combines both the sharp Poincar\\'e inequality and the sharp Rellich inequality or the sharp Sobolev inequality for $\\Delta_g$ in $\\mathbb H^n$. As a consequence, we obtain the Poincar\\'e--Sobolev inequ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.02055","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"}