Lp Fourier multipliers on compact Lie groups

TL;DR

This paper extends Lp multiplier theorems to invariant and non-invariant operators on compact Lie groups, providing new insights and applications, including refined results for tori and a-priori estimates for certain operators.

Contribution

It establishes new Lp multiplier theorems for compact Lie groups, generalizing classical results and offering refinements and applications in analysis.

Findings

Lp multiplier theorems proven for compact Lie groups

Refinement of classical multiplier theorem on tori

Applications to a-priori estimates for non-hypoelliptic operators

Abstract

In this paper we prove Lp multiplier theorems for invariant and non-invariant operators on compact Lie groups in the spirit of the well-known Hormander-Mikhlin theorem on Rn and its variants on tori Tn. We also give applications to a-priori estimates for non-hypoelliptic operators. Already in the case of tori we get an interesting refinement of the classical multiplier theorem.