Smooth operators for the regular representation on homogeneous spaces
Volume 142 / 2000
Studia Mathematica 142 (2000), 149-157
DOI: 10.4064/sm-142-2-149-157
Abstract
A necessary and sufficient condition for a bounded operator on $L^2(M)$, M a Riemannian compact homogeneous space, to be smooth under conjugation by the regular representation is given. It is shown that, if all formal 'Fourier multipliers with variable coefficients' are bounded, then they are also smooth. In particular, they are smooth if M is a rank-one symmetric space.
