# Boundedness of Pseudodifferential Operators with symbols in Wiener amalgam spaces on Modulation Spaces

## TL;DR

This paper establishes conditions under which Weyl operators with symbols in Wiener amalgam spaces are bounded on modulation spaces, linking these symbol classes to operator boundedness in a novel way.

## Contribution

It provides the first known results connecting Wiener amalgam space symbols to bounded Weyl operators on classical modulation spaces.

## Key findings

- Weyl operators with Wiener amalgam space symbols are bounded on modulation spaces under certain conditions
- New theoretical link between Wiener amalgam spaces and modulation space operator boundedness
- First result relating these specific symbol classes to operator behavior

## Abstract

This paper provides sufficient conditions for the boundedness of Weyl operators on modulation spaces. The Weyl symbols belong to Wiener amalgam spaces, or generalized modulation spaces, as recently renamed by their inventor Hans Feichtinger. This is the first result which relates symbols in Wiener amalgam spaces to operators acting on classical modulation spaces.