{"paper":{"title":"On restrictions of Besov functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Julien Brasseur (I2M)","submitted_at":"2017-06-14T13:01:35Z","abstract_excerpt":"In this paper, we study the smoothness of restrictions of Besov functions. It is known that for any $f\\in B\\_{p,q}^s(\\mathbb{R}^N)$ with $q\\leq p$ we have $f(\\cdot,y)\\in B\\_{p,q}^s(\\mathbb{R}^d)$ for a.e. $y\\in \\mathbb{R}^{N-d}$. We prove that this is no longer true when $p\\<q$. Namely, we construct a function $f\\in B\\_{p,q}^s(\\mathbb{R}^N)$ such that $f(\\cdot,y)\\notin B\\_{p,q}^s(\\mathbb{R}^d)$ for a.e. $y\\in \\mathbb{R}^{N-d}$. We show that, in fact, $f(\\cdot,y)$ belong to $B\\_{p,q}^{(s,\\Psi)}(\\mathbb{R}^d)$ for a.e. $y\\in\\mathbb{R}^{N-d}$, a Besov space of generalized smoothness, and, when $q"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04462","kind":"arxiv","version":2},"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"}