Pietsch-Maurey-Rosenthal factorization of summing multilinear operators

[EN] The main purpose of this paper is the study of a new class of summing mul-tilinear operators acting from the product of Banach lattices with some nontrivial lattice convexity. A mixed Pietsch-Maurey-Rosenthal type factorization theorem for these opera-tors is proved under weaker convexity requirements than the ones that are needed in the Maurey-Rosenthal factorization through products of Lq-spaces. A by-product of our fac-torization is an extension of multilinear operators de¿ned by a q-concavity type property to a product of special Banach function lattices which inherit some lattice-geometric prop-erties of the domain spaces, as order continuity and p-convexity. Factorization through Fremlin¿s tensor products is also analyzed. Applications are presented to study a special class of linear operators between Banach function lattices that can be characterized by a strong version of q-concavity. This class contains q-dominated operators, and so the obtained results provide a new factorization theorem for operators from this class.