A necessary and sufficient condition for a bounded operator on , 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.
@article{bwmeta1.element.bwnjournal-article-smv142i2p149bwm,
author = {Severino Melo},
title = {Smooth operators for the regular representation on homogeneous spaces},
journal = {Studia Mathematica},
volume = {141},
year = {2000},
pages = {149-157},
zbl = {0978.47037},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv142i2p149bwm}
}
Melo, Severino. Smooth operators for the regular representation on homogeneous spaces. Studia Mathematica, Tome 141 (2000) pp. 149-157. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv142i2p149bwm/
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