On RR^n It is well known that the fourier transform is strong (p,p) for p in (1,infty). Is Carleson's Theorem true for nonabelian compact groups? Is it true for locally compact abelian groups? What is the state of the art? Does there exists some type of Calderon-Zymund decomposition for f in L^1(G) when G is a locally compact topological group?