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Weighted inequalities ‖f‖q,ν,B0 ≤ C ∑n j=1 ‖fxj‖p,ωj ,B0 of Sobolev type (supp f ⊂ B0) and of Poincaré type (f̄ν,B0 = 0) are studied, with different weight functions for each partial derivative fxj , for parallelepipeds B0 ⊂ En, n ≥ 1. Also, weighted inequalities ‖f‖q,ν ≤ C‖Xf‖p,ω of the same type are considered for vector fields X = {Xj}, j = 1, . . . , m, with infinitely differentiable coefficients satisfying the Hörmander condition. §

On some nonuniform cases of the weighted Sobolev and Poincaré inequalities