Norms of complex harmonic projection operators

In this paper we estimate the (L(P) - L(2))-norm of the complex harmonic projectors pi_(ll'), for p between 1 and 2, uniformly with respect to the indexes l, l'. We provide sharp estimates both for the projectors pi_(ll'), when l, l' belong to a proper angular sector in N x N, and for the projectors pi_(l0) and pi_(0l). The proof is based on an extension of a complex interpolation argument by C. Sogge. In the appendix, we prove in a direct way the uniform boundedness; of a particular zonal kernel in the L(1) norm on the unit sphere of R(2n).