{"paper":{"title":"Besov spaces via hyperbolic fillings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Tom\\'as Soto","submitted_at":"2016-06-26T20:25:35Z","abstract_excerpt":"We establish a new characterization of the homogeneous Besov spaces $\\dot{\\mathcal B}^{s}_{p,q}(Z)$ with smoothness $s \\in (0,1)$ in the setting of doubling metric measure spaces $(Z,d,\\mu)$. The characterization is given in terms of a hyperbolic filling of the metric space $(Z,d)$, a construction which has previously appeared in the context of other function spaces in [3,1,2]. We use the characterization to obtain results concerning the density of Lipschitz functions in the spaces $\\dot{\\mathcal B}^{s}_{p,q}(Z)$ and a general complex interpolation formula in the smoothness range $0 < s < 1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.08082","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"}