# Wiener estimates on modulation spaces

## TL;DR

This paper characterizes modulation spaces using Wiener estimates on short-time Fourier transforms and refines formulas for periodic distributions with Lebesgue coefficient estimates.

## Contribution

It introduces Wiener estimates as a new characterization tool for modulation spaces and improves existing formulas for periodic distributions.

## Key findings

- Modulation spaces characterized by Wiener estimates.
- Refined formulas for periodic distributions.
- Enhanced understanding of Fourier coefficients in distribution spaces.

## Abstract

We characterise modulation spaces by suitable Wiener estimates on the short-time Fourier transforms of the involved functions and distributions. We use the results to refine some formulae on periodic distributions with Lebesgue estimates on their coefficients.