{"paper":{"title":"Geometric Hardy and Hardy-Sobolev inequalities on Heisenberg groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bolys Sabitbek, Durvudkhan Suragan, Michael Ruzhansky","submitted_at":"2018-11-17T15:33:32Z","abstract_excerpt":"In this paper, we present the geometric Hardy inequality for the sub-Laplacian in the half-spaces on the stratified groups. As a consequence, we obtain the following geometric Hardy inequality in a half-space on the Heisenberg group with a sharp constant\n  \\begin{equation*}\n  \\int_{\\mathbb{H}^+} |\\nabla_{H}u|^p d\\xi \\geq \\left(\\frac{p-1}{p}\\right)^p \\int_{\\mathbb{H}^+} \\frac{\\mathcal{W}(\\xi)^p}{dist(\\xi,\\partial \\mathbb{H}^+)^p} |u|^p d\\xi, \\,\\, p>1,\n  \\end{equation*}\n  which solves the conjecture in the paper \\cite{Larson}. Also, we obtain a version of the Hardy-Sobolev inequality in a half-s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.07181","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"}