We estimate the truncated double trigonometric series
∑n=oN∑m=oMamne2πι(mx+ny),amn∈C, in Lebesgue spaces with mixed norms in terms of the pth−qth power finite double sums of its coefficients. We obtain these estimates for all possible values of the exponents involved and we provide examples of matrices in cM×N that maximize some of them up to a constant independent of M and N. We also handle the more general case where the oscillatory factors in the sum terms are not orthogonal in either variable.