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arXiv · 0909.1339

Weighted multilinear Poincare inequalities for vector fields of Hormander type

Diego Maldonado·Kabe Moen·Virginia Naibo
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Abstract

As the classical $(p,q)$-Poincaré inequality is known to fail for $0 < p < 1$, we introduce the notion of weighted multilinear Poincaré inequality as a natural alternative when $m$-fold products and $1/m < p$ are considered. We prove such weighted multilinear Poincaré inequalities in the subelliptic context associated to vector fields of Hörmader 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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Diego Maldonado, Kabe Moen, Virginia Naibo. 2010-02-22. Weighted multilinear Poincare inequalities for vector fields of Hormander type. https://arxiv.org/abs/0909.1339

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