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We introduce a notion of $(p,q)$-dominated multilinear operators which stemsfrom the geometrical approach provided by $\Sigma$-operators. We prove that$(p,q)$-dominated multilinear operators can be characterized in terms of theirbehavior on finite sequences and in terms of their relation with a Laprest\'etensor norm. We also prove that they verify a generalization of the Pietsch'sDomination Theorem and Kwapie\'n's Factorization Theorem. Also, we study thecollection $\mathcal{D}_{p,q}$ of all $(p,q)$-dominated multilinear operatorsshowing that $\mathcal{D}_{p,q}$ has a maximal ideal demeanor and that theLaprest\'e norm has a finitely generated behavior.

$(p,q)$-Dominated Multilinear Operators and Laprest\'e tensor norms