Dans cet article nous prouvons des inégalités de Poincaré associées à une famille de champs de vecteurs satisfaisant l’hypothèse de Hörmander et qui sont aussi nouvelles dans le cas sans poids. Nous obtenons une nouvelle formule de représentation pour une fonction en termes des champs de vecteurs appliqués à la fonction. En particulier, on en déduit une inégalité isopérimétrique relative.
We derive weighted Poincaré inequalities for vector fields which satisfy the Hörmander condition, including new results in the unweighted case. We also derive a new integral representation formula for a function in terms of the vector fields applied to the function. As a corollary of the versions of Poincaré’s inequality, we obtain relative isoperimetric inequalities.
@article{AIF_1995__45_2_577_0,
author = {Franchi, Bruno and Lu, Guozhen and Wheeden, Richard L.},
title = {Representation formulas and weighted Poincar\'e inequalities for H\"ormander vector fields},
journal = {Annales de l'Institut Fourier},
volume = {45},
year = {1995},
pages = {577-604},
doi = {10.5802/aif.1466},
mrnumber = {96i:46037},
zbl = {0820.46026},
language = {en},
url = {http://dml.mathdoc.fr/item/AIF_1995__45_2_577_0}
}
Franchi, Bruno; Lu, Guozhen; Wheeden, Richard L. Representation formulas and weighted Poincaré inequalities for Hörmander vector fields. Annales de l'Institut Fourier, Tome 45 (1995) pp. 577-604. doi : 10.5802/aif.1466. http://gdmltest.u-ga.fr/item/AIF_1995__45_2_577_0/
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