STRONG DIFFERENTIAL SUBORDINATES FOR NONCOMMUTATIVE SUBMARTINGALES

• 成果类型: Article
• 署名作者: Jiao, Yong; Osekowski, Adam; Wu, Lian
• 署名单位: Central South University; University of Warsaw
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/18-AOP1334
• 发表日期: 2019
• 页码: 3108-3142
• 关键词: sharp inequalities; beurling-ahlfors; martingales

摘要

We introduce a notion of strong differential subordination of noncommutative semimartingales, extending Burkholder's definition from the classical case (Ann. Probab. 22 (1994) 995-1025). Then we establish the maximal weak-type (1, 1) inequality under the additional assumption that the dominating process is a submartingale. The proof rests on a significant extension of the maximal weak-type estimate of Cuculescu and a Gundy-type decomposition of an arbitrary noncommutative submartingale. We also show the corresponding strong-type (p, p) estimate for 1 < p < infinity under the assumption that the dominating process is a nonnegative submartingale. This is accomplished by combining several techniques, including interpolationflavor method, Doob-Meyer decomposition and noncommutative analogue of good-. inequalities.