{"paper":{"title":"Dimension-free estimates for semigroup BMO and $A_p$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Leonid Slavin, Pavel Zatitskii","submitted_at":"2019-08-07T12:49:48Z","abstract_excerpt":"Let $K_t$ be either the heat or the Poisson kernel on $\\mathbb{R}^n.$ Let $\\mathcal{A}$ stand either for BMO equipped with the quadratic seminorm or for $A_p,$ $1< p\\le\\infty.$ We establish the following transference between the class $\\mathcal{A}$ on an interval $I\\subset\\mathbb{R}$ and its $K$-version, $\\mathcal{A}^K,$ on $\\mathbb{R}^n$: If a given integral functional admits an estimate on $\\mathcal{A}(I),$ then the same estimate holds for $\\mathcal{A}^K(\\mathbb{R}^n),$ with all Lebesgue averages replaced by $K$-averages. In particular, all such estimates are dimension-free. As an applicatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.02602","kind":"arxiv","version":2},"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/1908.02602/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"}