IUMJ

Title: Weighted multilinear Poincare inequalities for vector fields of Hoermander type

Authors: Diego Maldonado, Kabe Moen and Virginia Naibo

Issue: Volume 60 (2011), Issue 2, 473-506

Abstract:

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.