{"paper":{"title":"On the Bourgain--Brezis--Mironescu spaces over Carleson tents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"\\'Arp\\'ad B\\'enyi, Bingyang Hu, Xiaojing Zhou","submitted_at":"2026-06-26T17:36:55Z","abstract_excerpt":"We introduce Carleson analogs of the Bourgain--Brezis--Mironescu spaces $B$ and $B_0$ by measuring mean oscillation over upper Carleson tents. For these spaces, denoted by $B_{\\mathcal C}^p$ and $B_{\\mathcal C,0}^p$, we prove two types of structural results. First, we show that they contain several natural classes of functions, including BMO/VMO--Carleson spaces, tent-space potential classes, and fractional Sobolev classes. Second, motivated by Zhu's structural theorem for BMO spaces induced by the Bergman metric, we establish decompositions of $B_{\\mathcal C}^p$ and $B_{\\mathcal C,0}^p$ into "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.28292","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.28292/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"}