{"paper":{"title":"Noncommutative Davis type decompositions and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.OA"],"primary_cat":"math.PR","authors_text":"Lian Wu, Narcisse Randrianantoanina, Quanhua Xu","submitted_at":"2017-12-04T21:25:20Z","abstract_excerpt":"We prove the noncommutative Davis decomposition for the column Hardy space $\\H_p^c$ for all $0<p\\leq 1$. A new feature of our Davis decomposition is a simultaneous control of $\\H_1^c$ and $\\H_q^c$ norms for any noncommutative martingale in $\\H_1^c \\cap \\H_q^c$ when $q\\geq 2$. As applications, we show that the Burkholder/Rosenthal inequality holds for bounded martingales in a noncommutative symmetric space associated with a function space $E$ that is either an interpolation of the couple $(L_p, L_2)$ for some $1<p<2$ or is an interpolation of the couple $(L_2, L_q)$ for some $2<q<\\infty$. We al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.01374","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":""},"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"}