Central Fourier analysis for Lorentz spaces on compact Lie groups
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.
scientific article; zbMATH DE number 4113235