2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/219496Let H be a regular element of an irreducible Lie Algebra g, and let mu be the orbital measure supported on the Adjoint orbit of H. We show that the k-th power of the Fourier transform of mu is in L^2(g) if and only if k > dim g/(dim g-rank g).Functional Analysis58C35; 22E60; 43A70text