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December 21, 2025Open Access

Hardy-Littlewood maximal operator on spaces of exponential volume growth

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Authors

KFKoji FujiwaraANAmos Nevo

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Overview

This analysis reveals weak-type maximal inequalities in discrete groups, indicating connections to regular representations and braid groups.

Key Points

  • This research aims to investigate the Hardy-Littlewood maximal function in discrete groups with specific geometric structures.
  • Examined invariant metrics associated with discrete groups and explored their radial structures.
  • Established a weak-type maximal inequality under certain geometric conditions.
  • Analyzed connections to geometric group theory and representations.
  • Found weak-type maximal inequalities for various group structures.
  • Demonstrated the behavior of the maximal operator in right-angled Artin and braid groups.
  • Derived optimal maximal inequalities for non-elementary word-hyperbolic groups.

Cite This Study

Fujiwara et al. (2025) studied this question.

synapsesocial.com/papers/69473b64db9c958d0dfca9ddhttps://doi.org/10.48550/arxiv.2505.07682
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