{"paper":{"title":"The existence of a global fundamental solution for homogeneous H\\\"ormander operators via a global lifting method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrea Bonfiglioli, Stefano Biagi","submitted_at":"2016-04-09T19:40:44Z","abstract_excerpt":"We prove the existence of a global fundamental solution $\\Gamma(x;y)$ (with pole $x$) for any H\\\"ormander operator $\\mathcal{L}=\\sum_{i=1}^m X_i^2$ on $\\mathbb{R}^n$ which is $\\delta$-homogeneous of degree $2$. By means of a global Lifting method for homogeneous operators proved by Folland in [On the Rothschild-Stein lifting theorem, Comm. PDEs, 1977], there exists a Carnot group $\\mathbb{G}$ and a polynomial surjective map $\\pi:\\mathbb{G}\\to \\mathbb{R}^n$ such that $\\mathcal{L}$ is $\\pi$-related to a sub-Laplacian $\\mathcal{L}_{\\mathbb{G}}$ on $\\mathbb{G}$. We show that it is always possible "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02599","kind":"arxiv","version":3},"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"}