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Displaying similar documents to “The sharp Poincaré inequality for free vector fields: an endpoint result.”

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...

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 L 1 versions of Poincaré’s inequality, we obtain relative isoperimetric inequalities.

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.

Compact embedding theorems for generalized Sobolev spaces

Maria Manfredini (1993)

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 give some compact embedding theorems for Sobolev spaces, related to m -tuples of vectors fields of C 1 class on R N .