{"paper":{"title":"H\\\"older continuity of functions in the fractional Sobolev spaces: 1-dimensional case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yan Rybalko","submitted_at":"2023-08-11T09:52:22Z","abstract_excerpt":"This paper deals with the embedding of the Sobolev spaces of fractional order into the space of H\\\"older continuous functions. More precisely, we show that the function $f\\in H^s(\\mathbb{R})$ with $\\frac{1}{2}<s<1$ is H\\\"older continuous with the exponent $s-\\frac{1}{2}$. This is a particular case of the much stronger embedding theorems (see Section 2.8.1 in \\textit{H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland Pub. Co., Amsterdam, 1978.}), but here we give an elementary proof for $H^{s}(\\mathbb{R})$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.06048","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2308.06048/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}