# Noncommutative harmonic analysis on semigroups

## TL;DR

This paper develops noncommutative harmonic analysis tools on semigroups, including multiplier theorems and maximal inequalities, leading to ergodic theorems that extend classical results and simplify existing proofs.

## Contribution

It introduces new noncommutative multiplier theorems and maximal inequalities on semigroups, extending classical harmonic analysis results to the noncommutative setting.

## Key findings

- Established noncommutative multiplier theorems
- Proved maximal inequalities for semigroups
- Derived ergodic theorems in the noncommutative context

## Abstract

In this paper we obtain some noncommutative multiplier theorems and maximal inequalities on semigroups. As applications, we obtain the corresponding individual ergodic theorems. Our main results extend some classical results of Stein and Cowling on one hand, and simplify the main arguments of Junge-Le Merdy-Xu's related work [15].