Fourier multipliers for Triebel–Lizorkin spaces on compact Lie groups
Fourier multipliers for Triebel–Lizorkin spaces on compact Lie groups
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 Hörmander-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 Hörmander-Mihlin …