  In this paper we prove a plenty of new results concerning summabililty
properties of multilinear mappings between Banach spaces, such as an extension
of Littlewood's 4/3 Theorem. Among other features, it is shown that every
continuous n-linear form on the disc algebra or the Hardy space is
(1;2,...,2)-summing, the role of the Littlewood-Orlicz property in the theory
is established and the interplay with almost summing multilinear mappings is
explored.
