Weighted multilinear Poincare inequalities for vector fields of Hormander type

2009/09/07 by Diego Maldonado, Kabe Moen, Maldonado, Diego +3
Mathematics · #26D10 #31B10 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.0909.1339

openalex publication_date 2009/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• New maximal functions and multiple weights for the multilinear Calderón–Zygmund theory

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