By combining some results of C. S. Herz on the Fourier algebra with the notion of contractions of Lie groups, we prove theorems which allow transference of multipliers either from the Lie algebra or from the Cartan motion group associated to a compact Lie group to the group itself.
It is shown that if is a connected metrizable compact Abelian group and , any (possibly discontinuous) translation invariant linear form on is a scalar multiple of the Haar measure. This result extends the theorem of G.H. Meisters and W.M. Schmidt (J. Funct. Anal. 13 (1972), 407-424) on . Our method permits in fact to consider any superreflexive translation invariant Banach lattice on , which is the adopted point of view. We study the representation of an element of this invariant lattice...
By a Fourier multiplier technique on Cantor-like Abelian groups with characters of finite order, the norms from L² into of certain embeddings of character sums are computed. It turns out that the orders of the characters are immaterial as soon as they are at least four.