Notes on bilinear lattice bump Fourier multipliers

TL;DR

This paper studies bilinear Fourier multipliers with bump function multipliers and establishes transference theorems in amalgam and Wiener amalgam spaces.

Contribution

It introduces two transference theorems for bilinear Fourier multipliers with bump function multipliers in different function spaces.

Findings

Proves transference theorems in amalgam spaces.

Proves transference theorems in Wiener amalgam spaces.

Abstract

We consider the bilinear Fourier multiplier operator with the multiplier written as a linear combination of a fixed bump function. For those operators we prove two transference theorems, one in amalgam spaces and the other in Wiener amalgam spaces.