Unified Grothendieck's and Kwapien's Theorems for Multilinear Operators

Kwapie ' n's theorem asserts that every continuous linear operator from l(1) to l(p) is absolutely (r, 1)-summing for 1/r = 1 - |1/ p - 1/2|. When p = 2 it recovers the famous Grothendieck's theorem. In this paper we investigate multilinear variants of these theorems and related issues. Among other results we present a unified version of Kwapie ' n's and Grothendieck's results that encompasses the cases of multiple summing and absolutely summing multilinear operators.