{"paper":{"title":"On strongly orthogonal martingales in UMD Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.FA"],"primary_cat":"math.PR","authors_text":"Ivan Yaroslavtsev","submitted_at":"2018-12-19T16:05:43Z","abstract_excerpt":"In the present paper we introduce the notion of strongly orthogonal martingales. Moreover, we show that for any UMD Banach space $X$ and for any $X$-valued strongly orthogonal martingales $M$ and $N$ such that $N$ is weakly differentially subordinate to $M$ one has that for any $1<p<\\infty$ \\[ \\mathbb E \\|N_t\\|^p \\leq \\chi_{p, X}^p \\mathbb E \\|M_t\\|^p,\\;\\;\\; t\\geq 0, \\] with the sharp constant $\\chi_{p, X}$ being the norm of a decoupling-type martingale transform and being within the range \\[ \\max\\Bigl\\{\\sqrt{\\beta_{p, X}}, \\sqrt{\\hbar_{p,X}}\\Bigr\\} \\leq \\max\\{\\beta_{p, X}^{\\gamma,+}, \\beta_{p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.08049","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"}