{"paper":{"title":"On the Hausdorff dimension of continuous functions belonging to H\\\"older and Besov spaces on fractal d-sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Abel Carvalho, Ant\\'onio Caetano","submitted_at":"2010-12-30T20:02:07Z","abstract_excerpt":"The Hausdorff dimension of the graphs of the functions in H\\\"older and Besov spaces (in this case with integrability p \\geq 1) on fractal d-sets is studied. Denoting by s \\in (0,1] the smoothness parameter, the sharp upper bound min{d+1-s,d/s} is obtained. In particular, when passing from d \\geq s to d<s there is a change of behaviour from d+1-s to d/s which implies that even highly nonsmooth functions defined on cubes in R^n have not so rough graphs when restricted to, say, \\emp{rarefied} fractals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.0147","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"}