Sharp results for the Weyl product on modulation spaces

TL;DR

This paper establishes precise conditions under which the Weyl product is bounded on modulation spaces, also deriving sharp bounds for twisted convolution on Wiener amalgam spaces, advancing the understanding of these operators in harmonic analysis.

Contribution

It provides the first complete characterization of Lebesgue exponents for boundedness of the Weyl product on modulation spaces, including sharp bounds for twisted convolution.

Findings

Necessary and sufficient conditions for Weyl product boundedness

Sharp bounds for twisted convolution on Wiener amalgam spaces

Extension of results from N=2 to general N for Weyl products

Abstract

We give sufficient and necessary conditions on the Lebesgue exponents for the Weyl product to be bounded on modulation spaces. The sufficient conditions are obtained as the restriction to $N=2$ of a result valid for the $N$-fold Weyl product. As a byproduct, we obtain sharp conditions for the twisted convolution to be bounded on Wiener amalgam spaces.