{"paper":{"title":"Global estimates in Sobolev spaces for homogeneous H\\\"ormander sums of squares","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrea Bonfiglioli, Marco Bramanti, Stefano Biagi","submitted_at":"2019-06-18T22:43:29Z","abstract_excerpt":"Let $\\mathcal{L}=\\sum_{j=1}^m X_j^2$ be a H\\\"ormander sum of squares of vector fields in space $\\mathbb{R}^n$, where any $X_j$ is homogeneous of degree $1$ with respect to a family of non-isotropic dilations in space. In this paper we prove global estimates and regularity properties for $\\mathcal{L}$ in the $X$-Sobolev spaces $W^{k,p}_X(\\mathbb{R}^n)$, where $X = \\{X_1,\\ldots,X_m\\}$. In our approach, we combine local results for general H\\\"ormander sums of squares, the homogeneity property of the $X_j$'s, plus a global lifting technique for homogeneous vector fields."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.07835","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"}