Absolutely summing multilinear operators via interpolation

We use an interpolative technique from [1] to introduce the notion of multiple N-separately summing operators. Our approach extends and unifies some recent results; for instance we recover the best known estimates of the multilinear Bohnenblust-Hille constants due to F. Bayart, D. Pellegrino and J. Seoane-Sepulveda. More precisely, as a consequence of our main result, for 1 <= t < 2 and m > 1 we prove that (Sigma(infinity)(i1,...,im=1) vertical bar U (e(i1), ... , e(im))vertical bar(2tm/2+(m-1)t))(2+(m-1)t/2tm) <= [Pi(m)(j=2) Gamma (2 - 2 - t/jt - 2t + 2)(t(j-2)+2/2t-2jt)] parallel to U parallel to for all complex m-linear forms U: c(0) x ... x c(0) --> C. (C) 2015 Elsevier Inc. All rights reserved.