Transference of bilinear multiplier operators on Lorentz spaces

TL;DR

This paper establishes a transference theorem for bilinear multiplier operators on Lorentz spaces, linking boundedness properties between the real line and the torus, extending classical results to a broader functional setting.

Contribution

It introduces a DeLeeuw type theorem for modulation invariant multipliers on Lorentz spaces, broadening the scope of transference principles in harmonic analysis.

Findings

Proves boundedness transference between real line and torus for bilinear multipliers.

Extends classical DeLeeuw theorem to Lorentz space setting.

Provides tools for analyzing modulation invariant operators in advanced function spaces.

Abstract

We prove a DeLeeuw type theorem of transference of boundedness for modulation invariant multiplier operators between the groups defined by the real line and the torus.