{"paper":{"title":"On the Rademacher maximal function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mikko Kemppainen","submitted_at":"2009-12-17T10:24:33Z","abstract_excerpt":"This paper studies a new maximal operator introduced by Hyt\\\"onen, McIntosh and Portal in 2008 for functions taking values in a Banach space. The L^p-boundedness of this operator depends on the range space; certain requirements on type and cotype are present for instance. The original Euclidean definition of the maximal function is generalized to sigma-finite measure spaces with filtrations and the L^p-boundedness is shown not to depend on the underlying measure space or the filtration. Martingale techniques are applied to prove that a weak type inequality is sufficient for L^p-boundedness and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.3358","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}