John-Nirenberg inequality and atomic decomposition for noncommutative martingales

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• 作者：Guixiang Hong^a ; ¹ ; ^{guixiang.hong@univ-fcomte.fr} ; Tao Mei^b ; ² ; ^{mei@wayne.edu}
• 关键词：Noncommutative Lp-spaces ; Hardy spaces and BMO spaces ; Noncommutative martingales ; John&ndash ; Nirenberg inequality ; Atomic decomposition
• 刊名：Journal of Functional Analysis
• 出版年：2012
• 期刊代码：75_00221236
• 类别：mt
• 出版时间：15 August, 2012
• 卷：263
• 期：4
• 页码：1064-1097
• 文件大小：256 K

摘要

In this paper, we study the John-Nirenberg inequality for and the atomic decomposition for of noncommutative martingales. We first establish a crude version of the column (resp. row) John-Nirenberg inequality for all . By an extreme point property of -space for , we then obtain a fine version of this inequality. The latter corresponds exactly to the classical John-Nirenberg inequality and enables us to obtain an exponential integrability inequality like in the classical case. These results extend and improve Junge and Musat始s John-Nirenberg inequality. By duality, we obtain the corresponding q-atomic decomposition for different Hardy spaces for all , which extends the 2-atomic decomposition previously obtained by Bekjan et al. Finally, we give a negative answer to a question posed by Junge and Musat about .