Transferring Fourier Multipliers from Rn to Compact Lie Groups

TL;DR

This paper demonstrates how to transfer Fourier multiplier bounds from Euclidean spaces to compact Lie groups using the wrapping map, leading to improved bounds and simplified proofs.

Contribution

It introduces a method to transfer Lp multiplier bounds from Rn to compact Lie groups, enhancing existing results and simplifying proofs.

Findings

Lp boundedness of multipliers on compact Lie groups established

Bounds improved in several cases

Simplified proofs for multiplier estimates

Abstract

This paper uses the wrapping map of Dooley and Wildberger to prove Lp boundedness of multipliers on compact Lie groups by transferring the estimate from Rn. This improves the bounds in several cases, and simplifies the proofs of others.