Representation formulas and weighted Poincaré inequalities for Hörmander vector fields
Bruno Franchi, Guozhen Lu, Richard L. Wheeden (1995)
Annales de l'institut Fourier
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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.