  We consider the Carleson embeddings of the classical Hardy spaces (on the
disk) into a L p ($\mu$) space, where $\mu$ is a Carleson measure on the unit
disk. This includes the case of composition operators. We characterize such
operators which are r-summing on H p , where p \textgreater{} 1 and r $\ge$ 1.
This completely extends the former results on the subject and solves a problem
open since the early seventies. Mathematics Subject Classification. Primary:
47B33 -- Secondary: 28A12; 30C85; 31A15; 46E20; 46E22; 47B06
