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Fourier multipliers for Triebel-Lizorkin spaces on compact Lie groups (2101.12314v2)
Published 28 Jan 2021 in math.FA, math.AP, and math.RT
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.