Absolutely continuous multilinear operators

We introduce the new class of the (p; p(1), ... , p(m); sigma)-absolutely continuous multilinear operators, that is defined using a summability property that provides the multilinear version of the (p, sigma)-absolutely continuous operators. We give an analogue of the Pietsch domination theorem and a multilinear version of the associated factorization theorem that holds for (p, sigma)-absolutely continuous operators, obtaining in this way a rich factorization theory. We present also a tensor norm which represents this multi-ideal by trace duality. As an application, we show that (p; p(1), ... , p(m); sigma)-absolutely continuous multilinear operators are compact under some requirements. Applications to factorization of linear maps on Banach function spaces through interpolation spaces are also given. (C) 2012 Elsevier Inc. All rights reserved.