Hormander型向量场的加权多线性Poincare不等式
Weighted multilinear Poincare inequalities for vector fields of Hormander type
摘要：
由于经典的$(p,q)$不等式对$0 < p < 1$是不成立的，我们引入了加权多线性Poincaré不等式的概念，作为考虑$m$ -重积和$1/m < p$的自然替代.我们证明了这样的加权多线性Poincaré不等式在次椭圆上下文相关的向量场的Hörmader型。我们这样做，通过建立多线性表示公式和加权估计的多线性潜在的空间齐型。
英文摘要：
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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