{"paper":{"title":"An Extrapolation of Operator Valued Dyadic Paraproducts","license":"","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"Tao Mei","submitted_at":"2007-09-26T18:12:08Z","abstract_excerpt":"We consider the dyadic paraproducts $\\pi_\\f$ on $\\T$ associated with an $\\M$-valued function $\\f.$ Here $\\T$ is the unit circle and $\\M$ is a tracial von Neumann algebra. We prove that their boundedness on $L^p(\\T,L^p(\\M))$ for some $1<p<\\infty $ implies their boundedness on $L^p(\\T,L^p(\\M))$ for all $1<p<\\infty$ provided $\\f$ is in an operator-valued BMO space. We also consider a modified version of dyadic paraproducts and their boundedness on $L^p(\\T,L^p(\\M))."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0709.4229","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"}