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arXiv · 2506.18589

Maximal inequalities for square functions and quantitative mean ergodic theorems associated to group metric measure spaces

Panchugopal Bikram·Diptesh Saha
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Abstract

In this article, we establish weighted strong and weak type inequalities for non-commutative square functions that naturally arise in the analysis of differences between ball averages and martingale sequences within the framework of group metric measure spaces. Then we use these maximal inequalities to prove a quantitative mean ergodic theorem. Our study extends classical harmonic analysis techniques to the non-commutative setting, revealing intricate interactions between group structures, operator-valued functions, and associated filtration systems.

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Panchugopal Bikram, Diptesh Saha. 2025-06-23. Maximal inequalities for square functions and quantitative mean ergodic theorems associated to group metric measure spaces. https://arxiv.org/abs/2506.18589

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