Noncommutative continuous differentially subordinate martingales and second-order Riesz transforms

• 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: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-025-01372-x
• 发表日期: 2025
• 页码: 1-34
• 关键词: weak type inequality; sharp inequalities; ahlfors

摘要

We introduce the notion of differential subordination in the context of noncommutative continuous-time martingales and show that for 2 < infinity this domination enforces the corresponding L-p bound between the two processes. As applications, we obtain best-order L-p inequalities for the second-order Riesz transforms on a class of group von Neumann algebras equipped with a conditionally negative length function. The proof relies on a novel stochastic representation of these second-order operators and reveals an interesting interplay between the cylindrical geometric Brownian motion, the crossed product and the cocycle law.