Norms of harmonic projection operators on compact Lie groups (Q1821994)

We give sharp estimates for the growth of the norms of the projection operators \(H_{\lambda}f=f*d_{\lambda}\chi _{\lambda}\), as operators from \(L^ p(G)\) to \(L^ 2(G)\), where G is a compact Lie group and \(1\leq p\leq 2\). These estimates are uniform for those weights \(\lambda\) such that \(\lambda +\rho\) lies in a proper subcone of the positive Weyl chamber.