{"paper":{"title":"Sobolev spaces on Lie groups: embedding theorems and algebra properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"Anita Tabacco, Marco M. Peloso, Maria Vallarino, Tommaso Bruno","submitted_at":"2018-04-26T16:30:33Z","abstract_excerpt":"Let $G$ be a noncompact connected Lie group, denote with $\\rho$ a right Haar measure and choose a family of linearly independent left-invariant vector fields $\\mathbf{X}$ on $G$ satisfying H\\\"ormander's condition. Let $\\chi$ be a positive character of $G$ and consider the measure $\\mu_\\chi$ whose density with respect to $\\rho$ is $\\chi$. In this paper, we introduce Sobolev spaces $L^p_\\alpha(\\mu_\\chi)$ adapted to $\\mathbf{X}$ and $\\mu_\\chi$ ($1<p<\\infty$, $\\alpha\\geq 0$) and study embedding theorems and algebra properties of these spaces. As an application, we prove local well-posedness and re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.10154","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"}