Displaying similar documents to “Representation formulas and weighted Poincaré inequalities for Hörmander vector fields”

Subelliptic Poincaré inequalities: the case p < 1.

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.

Weighted Poincaré and Sobolev inequalites for vector fields satisfying Hörmander's condition and applications.

Guozhen Lu (1992)

Revista Matemática Iberoamericana

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In this paper we mainly prove weighted Poincaré inequalities for vector fields satisfying Hörmander's condition. A crucial part here is that we are able to get a pointwise estimate for any function over any metric ball controlled by a fractional integral of certain maximal function. The Sobolev type inequalities are also derived. As applications of these weighted inequalities, we will show the local regularity of weak solutions for certain classes of strongly degenerate differential...

Two-weight Sobolev-Poincaré inequalities and Harnack inequality for a class of degenerate elliptic operators

Bruno Franchi, Cristian E. Gutiérrez, Richard L. Wheeden (1994)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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In this Note we prove a two-weight Sobolev-Poincaré inequality for the function spaces associated with a Grushin type operator. Conditions on the weights are formulated in terms of a strong A ∞ weight with respect to the metric associated with the operator. Roughly speaking, the strong A ∞ condition provides relationships between line and solid integrals of the weight. Then, this result is applied in order to prove Harnack's inequality for positive weak solutions of some degenerate elliptic...