We determine the critical indexes for the Lp,q uniform boundedness of the characters of a compact connected semisimple Lie group. These results show a basic difference between the simple and the semisimple case, a situation which does not appear when dealing with Lp spaces. We provide applications to the general theory of central functions on compact Lie groups. © 1989 Springer-Verlag.
Giulini, S., Travaglini, G. (1989). Central Fourier analysis for Lorentz spaces on compact Lie groups. MONATSHEFTE FÜR MATHEMATIK, 107(3), 207-215 [10.1007/BF01300344].
Central Fourier analysis for Lorentz spaces on compact Lie groups
TRAVAGLINI, GIANCARLO
1989
Abstract
We determine the critical indexes for the Lp,q uniform boundedness of the characters of a compact connected semisimple Lie group. These results show a basic difference between the simple and the semisimple case, a situation which does not appear when dealing with Lp spaces. We provide applications to the general theory of central functions on compact Lie groups. © 1989 Springer-Verlag.
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