The size of characters of compact Lie groups

Pointwise upper bounds for characters of compact, connected, simple Lie groups are obtained which enable one to prove that if mu is any central, continuous measure and n exceeds half the dimension of the Lie group, then mu(n) is an element of L-1. When mu is a continuous, orbital measure then mu(n) is seen to belong to L-2. Lower bounds on the p-norms of characters are also obtained, and are used to show that, as in the abelian case, m-fold products of Sidon sets are not p-Sidon if p < 2m/(m + 1).