{"paper":{"title":"Sobolev algebras on nonunimodular Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Marco M. Peloso, Maria Vallarino","submitted_at":"2017-10-20T15:11:58Z","abstract_excerpt":"Let G be a noncompact connected Lie group and $\\rho$ be the right Haar measure of G. Let $X_1,...,X_q$ be a family of left invariant vector fields which satisfy H\\\"ormander's condition, and let $\\Delta=-\\sum_{i=1}^qX_i^2$ be the corresponding subLaplacian.\n  For $1\\leq p<\\infty$ and $\\alpha\\geq 0$ we define the Sobolev space $L^p_{\\alpha}(G)={f in L^p(\\rho): \\Delta^{\\alpha/2}f\\in L^p(\\rho) }$, endowed with the norm $\\|f\\|_{\\alpha,p}=\\|f\\|_{p}+\\|\\Delta^{\\alpha/2}f\\|_p$, where we denote by $\\|f\\|_p$ the norm of $f$ in $L^p(\\rho)$.\n  In this paper we show that for all $\\alpha\\geq 0$ and $p\\in (1,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.07566","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"}