On multipliers on compact Lie groups

TL;DR

This paper extends multiplier theorems to compact Lie groups, providing tools for analyzing pseudo-differential operators and non-hypoelliptic operators in Lp spaces, inspired by classical results on Euclidean spaces.

Contribution

It establishes Lp multiplier theorems for invariant and non-invariant operators on compact Lie groups, generalizing the Hormander-Mikhlin theorem.

Findings

Lp multiplier theorems for compact Lie groups

Applications to pseudo-differential operators

A-priori estimates for non-hypoelliptic operators

Abstract

In this note we announce 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. Applications are given to the mapping properties of pseudo-differential operators on Lp-spaces and to a-priori estimates for non-hypoelliptic operators.