Fourier multipliers for Triebel-Lizorkin spaces on compact Lie groups
Functional Analysis
2021-02-03 v2 Analysis of PDEs
Representation Theory
Abstract
We investigate the boundedness of Fourier multipliers on a compact Lie group when acting on Triebel-Lizorkin spaces. Criteria are given in terms of the H\"ormander-Mihlin-Marcinkiewicz condition. In our analysis, we use the difference structure of the unitary dual of a compact Lie group. Our results cover the sharp H\"ormander-Mihlin theorem on Lebesgue spaces and also other historical results on the subject.
Keywords
Cite
@article{arxiv.2101.12314,
title = {Fourier multipliers for Triebel-Lizorkin spaces on compact Lie groups},
author = {Duván Cardona and Michael Ruzhansky},
journal= {arXiv preprint arXiv:2101.12314},
year = {2021}
}
Comments
26 Pages. arXiv admin note: text overlap with arXiv:2101.05856