The sharp Poincaré inequality for free vector fields: an endpoint result.
Guozhen Lu (1994)
Revista Matemática Iberoamericana
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Guozhen Lu (1994)
Revista Matemática Iberoamericana
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Guozhen Lu (1996)
Publicacions Matemàtiques
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Oscar Salinas (1991)
Revista Matemática Iberoamericana
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The main purpose of this work is to obtain a Harnack inequality and estimates for the Green function for the general class of degenerate elliptic operators described below.
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.
Donatella Danielli, Nicola Garofalo, Duy-Minh Nhieu (1998)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Christoph J. Neugebauer (1991)
Publicacions Matemàtiques
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We prove weighted norm inequalities for the averaging operator Af(x) = 1/x ∫ f of monotone functions.
Stephen M. Buckley, Pekka Koskela, Guozhen Lu (1995)
Publicacions Matemàtiques
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We obtain (weighted) Poincaré type inequalities for vector fields satisfying the Hörmander condition for p < 1 under some assumptions on the subelliptic gradient of the function. Such inequalities hold on Boman domains associated with the underlying Carnot- Carathéodory metric. In particular, they remain true for solutions to certain classes of subelliptic equations. Our results complement the earlier results in these directions for p ≥ 1.
J. Michael Wilson (2003)
Publicacions Matemàtiques
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