{"paper":{"title":"Approximation and quasicontinuity of Besov and Triebel-Lizorkin functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Heli Tuominen, Pekka Koskela, Toni Heikkinen","submitted_at":"2015-05-21T11:38:30Z","abstract_excerpt":"We show that, for $0<s<1$, $0<p<\\infty$, $0<q<\\infty$, Haj\\l asz-Besov and Haj\\l asz-Triebel-Lizorkin functions can be approximated in the norm by discrete median convolutions. This allows us to show that, for these functions, the limit of medians, \\[ \\lim_{r\\to 0}m_u^\\gamma(B(x,r))=u^*(x), \\] exists quasieverywhere and defines a quasicontinuous representative of $u$. The above limit exists quasieverywhere also for Haj\\l asz functions $u\\in M^{s,p}$, $0<s\\le 1$, $0<p<\\infty$, but approximation of $u$ in $M^{s,p}$ by discrete (median) convolutions is not in general possible."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.05680","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"}