Abstract In this paper, we investigate noncommutative symmetric and asymmetric maximal inequalities associated with martingale transforms and fractional integrals. Our proofs depend on some recent advances on algebraic atomic decomposition and the noncommutative Gundy decomposition. We also prove several fractional maximal inequalities.

中文翻译：

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非交换鞅变换的最大不等式

摘要 在本文中，我们研究了与鞅变换和分数积分相关的非交换对称和非对称极大不等式。我们的证明依赖于最近在代数原子分解和非对易 Gundy 分解方面的一些进展。我们还证明了几个分数极大不等式。