Weighted multilinear Poincare inequalities for vector fields of Hoermander type Diego MaldonadoKabe MoenVirginia Naibo 26D1031B1046E35sub-elliptic Poincare inequalitiesmultilinear operatorsHoermander vector field: As the classical $(p,q)$-Poincar\'e inequality is known to fail for $0 < p < 1$, we introduce the notion of weighted multilinear Poincar\'e inequality as a natural alternative when $m$-fold products and $1/m < p$ are considered. We prove such weighted multilinear Poincar\'e inequalities in the subelliptic context associated to vector fields of H\"ormader type. We do so by establishing multilinear representation formulas and weighted estimates for multilinear potential operators in spaces of homogeneous type. Indiana University Mathematics Journal 2011 text pdf 10.1512/iumj.2011.60.4156 10.1512/iumj.2011.60.4156 en Indiana Univ. Math. J. 60 (2011) 473 - 506 state-of-the-art mathematics http://iumj.org/access/