{"paper":{"title":"The K\\\"othe dual of mixed Morrey spaces and applications","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Houkun Zhang, Jiang Zhou","submitted_at":"2022-04-01T15:19:41Z","abstract_excerpt":"In this paper, we study the separable and weak convergence of mixed-norm Lebesgue spaces. Furthermore, we prove that the block space $\\mathcal{B}_{\\vec{p}\\,'}^{p'_0}(\\mathbb{R}^n)$ is the K\\\"othe dual of the mixed Morrey space $\\mathcal{M}_{\\vec{p}}^{p_0}(\\mathbb{R}^n)$ by the Fatou property of these block spaces. The boundedness of the Hardy--Littlewood maximal function is further obtained on the block space $\\mathcal{B}_{\\vec{p}\\,'}^{p'_0}(\\mathbb{R}^n)$. As applications, the characterizations of $BMO(\\mathbb{R}^n)$ via the commutators of the fractional integral operator $I_{\\alpha}$ on mixe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.00518","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/2204.00518/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"}