完全不连通非交换群上Fejér均值的非交换极大不等式
A noncommutative maximal inequality for Fejér means on totally disconnected non-abelian groups
AI总结：
本文在完全不连通非交换紧群上，对共轭类不变的非交换L_p值函数建立了Fejér均值的非交换极大不等式，推广了Gát的经典结果，并显式计算了估计的界。
摘要：
本文探讨了在完全不连通非交换紧群G上取值的非交换L_p空间值函数的傅里叶分析。通过额外假设这些函数的值在每个共轭类内保持不变，我们利用G的关联特征系统建立了Fejér均值的非交换极大不等式。这是Gát经典结果的一个算子值版本。我们基本上遵循经典证明思路，但由于非交换性，许多经典论证需要修改。值得注意的是，与经典结果相比，我们估计的界被显式地计算出来。
英文摘要：
In this paper, we explore Fourier analysis for noncommutative $L_p$ space-valued functions on $G$, where $G$ is a totally disconnected non-abelian compact group. By additionally assuming that the value of these functions remains invariant within each conjugacy class, we establish a noncommutative maximal inequality for Fejér means utilizing the associated character system of $G$. This is an operator-valued version of the classical result due to Gát. We follow essentially the classical sketch, but due to the noncommutativity, many classical arguments have to be revised. Notably, compared to the classical results. the bounds of our estimates are explicity calculated.
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