{"paper":{"title":"Operator-Valued Hardy spaces and BMO Spaces on Spaces of Homogeneous Type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"Guixiang Hong, Wenhua Wang, Zhijie Fan","submitted_at":"2023-11-27T12:50:34Z","abstract_excerpt":"Let $\\mathcal{M}$ be a von Neumann algebra equipped with a normal semifinite faithful trace, $(\\mathbb{X},\\,d,\\,\\mu)$ be a space of homogeneous type in the sense of Coifman and Weiss, and $\\mathcal{N}=L_\\infty(\\mathbb{X})\\overline{\\otimes}\\mathcal{M}$. In this paper, we introduce and then conduct a systematic study on the operator-valued Hardy space $\\mathcal{H}_p(\\mathbb{X},\\,\\mathcal{M})$ for all $1\\leq p<\\infty$ and operator-valued BMO space $\\mathcal{BMO}(\\mathbb{X},\\,\\mathcal{M})$. The main results of this paper include $H_1$--$BMO$ duality theorem, atomic decomposition of $\\mathcal{H}_1("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.15775","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/2311.15775/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"}