{"paper":{"title":"Uncentered Fractional Maximal functions and mean oscillation spaces associated with dyadic Hausdorff content","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.AP","math.CA"],"primary_cat":"math.FA","authors_text":"Prasun Roychowdhury, Riju Basak, You-Wei Benson Chen","submitted_at":"2025-06-29T12:25:10Z","abstract_excerpt":"We study the action of uncentered fractional maximal functions on mean oscillation spaces associated with the dyadic Hausdorff content $\\mathcal{H}_{\\infty}^{\\beta}$ with $0<\\beta\\leq n$. For $0 < \\alpha < n$, we refine existing results concerning the action of the Euclidean uncentered fractional maximal function $\\mathcal{M}_{\\alpha}$ on the functions of bounded mean oscillations (BMO) and vanishing mean oscillations (VMO). In addition, for $0 < \\beta_1 \\leq \\beta_2 \\leq n$, we establish the boundedness of the $\\beta_2$-dimensional uncentered maximal function $\\mathcal{M}^{\\beta_2}$ on the sp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.23206","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/2506.23206/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"}