Interpolation and I¦-moment inequalities of noncommutative martingales

• 成果类型: Article
• 署名作者: Bekjan, Turdebek N.; Chen, Zeqian
• 署名单位: Chinese Academy of Sciences; Innovation Academy for Precision Measurement Science & Technology, CAS; Xinjiang University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-010-0319-2
• 发表日期: 2012
• 页码: 179-206
• 关键词: khintchine inequalities; THEOREM; SPACES; Extrapolation

摘要

This paper is devoted to the study of phi-moment inequalities for noncommutative martingales. In particular, we prove the noncommutative phi-moment analogues of martingale transformations, Stein's inequalities, Khintchine's inequalities for Rademacher's random variables, and Burkholder-Gundy's inequalities. The key ingredient is a noncommutative version of Marcinkiewicz type interpolation theorem for Orlicz spaces which we establish in this paper.