# Unimodular multipliers on $\alpha$-modulation spaces: A revisit with new method under weaker conditions

## TL;DR

This paper introduces a new method to analyze the boundedness of unimodular multipliers on lpha-modulation spaces, extending previous results to a broader class under weaker conditions.

## Contribution

It presents a novel approach based on Nicola--Primo--Tabacco's method, allowing boundedness results for a larger family of unimodular multipliers with fewer assumptions.

## Key findings

- Boundedness of unimodular multipliers established under weaker conditions
- Extended the class of multipliers for which boundedness holds
- Introduced a new analytical method for lpha-modulation spaces

## Abstract

By a new method derived from Nicola--Primo--Tabacco[24], we study the boundedness on $\alpha$-modulation spaces of unimodular multipliers with symbol $e^{i\mu(\xi)}$. Comparing with the previous results, the boundedness result is established for a larger family of unimodular multipliers under weaker assumptions.