Absolutely continuous multilinear operators

We introduce the new class of the (p;p1,…,pm;σ)-absolutely continuous multilinear operators, that is defined using a summability property that provides the multilinear version of the (p,σ)-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,σ)-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;p1,…,pm;σ)-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.