{"paper":{"title":"Subordination by orthogonal martingales in $L^{p}, 1<p\\le 2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander Volberg, Prabhu Janakiraman","submitted_at":"2010-12-04T20:59:21Z","abstract_excerpt":"We are given two martingales on the filtration of the two dimensional Brownian motion. One is subordinated to another. We want to give an estimate of $L^p$-norm of a subordinated one via the same norm of a dominating one. In this setting this was done by Burkholder in \\cite{Bu1}--\\cite{Bu8}. If one of the martingales is orthogonal, the constant should drop. This was demonstrated in \\cite{BaJ1}, when the orthogonality is attached to the subordinated martingale and when $2\\le p<\\infty$. This note contains an (almost obvious) observation that the same idea can be used in the case when the orthogo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.0948","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"}