{"paper":{"title":"Sobolev algebras through heat kernel estimates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Dorothee Frey, Fr\\'ed\\'eric Bernicot, Thierry Coulhon","submitted_at":"2015-05-06T17:37:46Z","abstract_excerpt":"On a doubling metric measure space $(M,d,\\mu)$ endowed with a \"carr\\'e du champ\", let $\\mathcal{L}$ be the associated Markov generator and $\\dot L^{p}_\\alpha(M,\\mathcal{L},\\mu)$ the corresponding homogeneous Sobolev space of order $0<\\alpha<1$ in $L^p$, $1<p<+\\infty$, with norm $\\left\\|\\mathcal{L}^{\\alpha/2}f\\right\\|_p$. We give sufficient conditions on the heat semigroup $(e^{-t\\mathcal{L}})_{t>0}$ for the spaces $\\dot L^{p}_\\alpha(M,\\mathcal{L},\\mu) \\cap L^\\infty(M,\\mu)$ to be algebras for the pointwise product. Two approaches are developed, one using paraproducts (relying on extrapolation t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.01442","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"}