# Continuity properties for Born-Jordan operators with symbols in H\"ormander classes and modulation spaces

## TL;DR

This paper establishes that Born-Jordan operators with symbols in H"ormander classes and modulation spaces retain their class properties, enabling the transfer of continuity and Schatten-von Neumann properties within the calculus.

## Contribution

It demonstrates that the Weyl symbol of a Born-Jordan operator remains in the same class as its Born-Jordan symbol for specific symbol classes, extending known properties.

## Key findings

- Weyl symbols of Born-Jordan operators stay in the same class as the original symbols.
- Continuity properties are preserved for Born-Jordan calculus.
- Schatten-von Neumann properties are transferable to Born-Jordan operators.

## Abstract

We show that the Weyl symbol of a Born-Jordan operator is in the same class as the Born-Jordan symbol, when H\"ormander symbols and certain types of modulation spaces are used as symbol classes. We use these properties to carry over continuity and Schatten-von Neumann properties to the Born-Jordan calculus.