Weighted multilinear Poincare inequalities for vector fields of Hormander type

Details Weighted multilinear Poincare inequalities for vector fields of Hormander type Weighted multilinear Poincare inequalities for vector fields of Hormander type

2009-09-07

arxiv.org/abs/0909.1339v2

Mathematics

Classical Analysis and ODEs

Minor typos corrected. To appear in Indiana Univ. Math. J

Scientific paper

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.

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