Conditioned square functions for noncommutative martingales

• 成果类型: Article
• 署名作者: Randrianantoanina, Narcisse
• 署名单位: University System of Ohio; Miami University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117906000000656
• 发表日期: 2007
• 页码: 1039-1070
• 关键词: function inequalities; random-variables; constants; interpolation; version; SPACES

摘要

We prove a weak-type (1, 1) inequality involving conditioned versions of square functions for martingales in noncommutative L-P-spaces associated with finite von Neumann algebras. As application, we determine the optimal orders for the best constants in the noncommutative Burkholder/Rosenthal inequalities from [Ann. Probab. 31 (2003) 948-995]. We also discuss BMO-norms of sums of noncommuting order-independent operators.