Weighted Multilinear Poincaré Inequalities for Vector Fields of Hörmander Type
نویسندگان
چکیده
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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