{"paper":{"title":"Embeddings of Besov Spaces on fractal h-sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Ant\\'onio Caetano, Dorothee Haroske","submitted_at":"2015-01-11T21:22:11Z","abstract_excerpt":"Let $\\Gamma$ be a fractal $h$-set and ${\\mathbb{B}}^{{\\sigma}}_{p,q}(\\Gamma)$ be a trace space of Besov type defined on $\\Gamma$. While we dealt in [9] with growth envelopes of such spaces mainly and investigated the existence of traces in detail in [12], we now study continuous embeddings between different spaces of that type on $\\Gamma$. We obtain necessary and sufficient conditions for such an embedding to hold, and can prove in some cases complete characterisations. It also includes the situation when the target space is of type $L_r(\\Gamma)$ and, as a by-product, under mild assumptions on"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02796","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"}