{"paper":{"title":"Square functions for noncommutative differentially subordinate martingales","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.PR"],"primary_cat":"math.OA","authors_text":"Dejian Zhu, Lian Wu, Narcisse Randrianantoanina, Yong Jiao","submitted_at":"2019-01-25T06:27:21Z","abstract_excerpt":"We prove inequalities involving noncommutative differentially subordinate martingales. More precisely, we prove that if $x$ is a self-adjoint noncommutative martingale and $y$ is weakly differentially subordinate to $x$ then $y$ admits a decomposition $dy=a +b +c$ (resp. $dy=z +w$) where $a$, $b$, and $c$ are adapted sequences (resp. $z$ and $w$ are martingale difference sequences) such that: $$ \\Big\\| (a_n)_{n\\geq 1}\\Big\\|_{L_{1,\\infty}({\\mathcal M}\\overline{\\otimes}\\ell_\\infty)} +\\Big\\| \\Big(\\sum_{n\\geq 1} \\mathcal{E}_{n-1}|b_n|^2 \\Big)^{{1}/{2}}\\Big\\|_{1, \\infty} + \\Big\\| \\Big(\\sum_{n\\geq 1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.08752","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"}