Boundedness of multilinear pseudo-differential operators on modulation spaces

TL;DR

This paper establishes boundedness conditions for multilinear pseudodifferential operators on modulation spaces, utilizing integrability conditions on their symbols' short-time Fourier transforms, and applies these results to Hilbert transforms.

Contribution

It introduces a new method for analyzing boundedness of multilinear operators on modulation spaces based on symbol transform integrability.

Findings

Boundedness results for multilinear pseudodifferential operators on modulation spaces.

Application of methods to bilinear and trilinear Hilbert transforms.

Demonstrates the effectiveness of the approach in specific operator cases.

Abstract

Boundedness results for multilinear pseudodifferential operators on products of modulation spaces are derived based on ordered integrability conditions on the short-time Fourier transform of the operators' symbols. The flexibility and strength of the introduced methods is demonstrated by their application to the bilinear and trilinear Hilbert transform.