{"paper":{"title":"Characterization of function spaces via low regularity mollifiers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Petru Mironescu, Xavier Lamy","submitted_at":"2014-04-26T23:43:06Z","abstract_excerpt":"Smoothness of a function $f:{\\mathbb R}^n\\to {\\mathbb R}$ can be measured in terms of the rate of convergence of $f\\ast\\rho_\\varepsilon$ to $f$, where $\\rho$ is an appropriate mollifier. In the framework of fractional Sobolev spaces, we characterize the \"appropriate\" mollifiers. We also obtain sufficient conditions, close to being necessary, which ensure that $\\rho$ is adapted to a given scale of spaces. Finally, we examine in detail the case where $\\rho$ is a characteristic function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.6695","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"}