We determine the critical indexes for the L^{p,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 L^p spaces. We provide applications to the general theory of central functions on compact Lie groups.
Central Fourier analysis for Lorentz spaces on compact Lie groups
GIULINI, SAVERIO;
1989
Abstract
We determine the critical indexes for the L^{p,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 L^p spaces. We provide applications to the general theory of central functions on compact Lie groups.
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