Relations between bilinear multipliers on $ \mathbb R^n, \mathbb{T}^n$ and $\mathbb{Z}^n$

TL;DR

This paper establishes a bilinear analogue of de Leeuw's theorem, connecting bilinear multipliers on Euclidean space, the torus, and the integer lattice, along with extension results.

Contribution

It introduces a bilinear version of de Leeuw's theorem and extends results for bilinear multipliers from periodic to more general settings.

Findings

Proved bilinear analogue of de Leeuw's theorem.

Extended Jodeit type results for bilinear multipliers.

Established connections between multipliers on different domains.

Abstract

In this paper we prove the bilinear analogue of de Leeuw's result for periodic bilinear multipliers and some Jodeit type extension results for bilinear multipliers.