{"paper":{"title":"New Martingale Inequalities and Applications to Fourier Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.PR"],"primary_cat":"math.CA","authors_text":"Dachun Yang, Ferenc Weisz, Guangheng Xie, Yong Jiao","submitted_at":"2018-10-11T13:26:05Z","abstract_excerpt":"Let $(\\Omega,\\mathcal{F},\\mathbb{P})$ be a probability space and $\\varphi:\\ \\Omega\\times[0,\\infty)\\to[0,\\infty)$ be a Musielak-Orlicz function. In this article, the authors prove that the Doob maximal operator is bounded on the Musielak-Orlicz space $L^{\\varphi}(\\Omega)$. Using this and extrapolation method, the authors then establish a Fefferman-Stein vector-valued Doob maximal inequality on $L^{\\varphi}(\\Omega)$. As applications, the authors obtain the dual version of the Doob maximal inequality and the Stein inequality for $L^{\\varphi}(\\Omega)$, which are new even in weighted Orlicz spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.05007","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"}