Transference of multilinear Fourier and Schur multipliers acting on non-commutative $L_p$-spaces for non-unimodular groups

TL;DR

This paper extends the transference results of multilinear Fourier and Schur multipliers from unimodular to non-unimodular groups within non-commutative $L_p$-spaces, broadening the applicability of these mathematical tools.

Contribution

It introduces a new definition for multilinear Fourier multipliers applicable to non-unimodular groups and proves that transference results hold in this broader context.

Findings

Transference results are valid for non-unimodular groups.

A new definition of multilinear Fourier multipliers for non-unimodular groups.

Extension of previous results to a more general setting.

Abstract

In arXiv:2206.00549, transference results between multilinear Fourier and Schur multipliers on noncommutative $L_p$-spaces were shown for unimodular groups. We propose a suitable extension of the definition of multilinear Fourier multipliers for non-unimodular groups, and show that the aforementioned transference results also hold in this more general setting.