ON SOME NONUNIFORM CASES OF THE WEIGHTED SOBOLEV AND POINCARE INEQUALITIES

Weighted inequalities parallel to f parallel to(q,nu,B0) <= C Sigma(n)(j=1) parallel to f(xj)parallel to(p,omega j,B0) of Sobolev type (supp f subset of B-0) and of Poincare type ((f) over bar (nu,B0) = 0) are studied, with different weight functions for each partial derivative f(xj), for parallelepipeds B-0 subset of E-n, n >= 1. Also, weighted inequalities parallel to f parallel to(q,nu) <= C parallel to X f parallel to(p,omega) of the same type are considered for vector fields X = {X-j}, j = 1,..., m, with infinitely differentiable coefficients satisfying the Hormander condition.