Multi-linear products with odd factors in pseudo-differential calculus with symbols in modulation spaces

TL;DR

This paper establishes conditions under which compositions of an odd number of pseudo-differential operators with symbols in modulation spaces are bounded, also applying to twisted convolutions on Wiener amalgam spaces.

Contribution

It provides new sufficient conditions for the boundedness of odd compositions of pseudo-differential operators with modulation space symbols and twisted convolutions.

Findings

Boundedness conditions for compositions of odd pseudo-differential operators

Boundedness criteria for twisted convolutions on Wiener amalgam spaces

Extension of modulation space symbol calculus

Abstract

We give sufficient conditions on the Lebesgue exponents for compositions of odd numbers of pseudo-differential operators with symbols in modulation spaces. As a byproduct, we obtain sufficient conditions for twisted convolutions of odd numbers of factors to be bounded on Wiener amalgam spaces.