Displaying similar documents to “Subelliptic Poincaré inequalities: the case p < 1.”

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.

Poincaré inequalities and Sobolev spaces.

Paul MacManus (2002)

Publicacions Matemàtiques

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Our understanding of the interplay between Poincaré inequalities, Sobolev inequalities and the geometry of the underlying space has changed considerably in recent years. These changes have simultaneously provided new insights into the classical theory and allowed much of that theory to be extended to a wide variety of different settings. This paper reviews some of these new results and techniques and concludes with an example on the preservation of Sobolev spaces by the maximal function. ...

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...

Bilipschitz embeddings of metric spaces into euclidean spaces.

Stephen Semmes (1999)

Publicacions Matemàtiques

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When does a metric space admit a bilipschitz embedding into some finite-dimensional Euclidean space? There does not seem to be a simple answer to this question. Results of Assouad [A1], [A2], [A3] do provide a simple answer if one permits some small ("snowflake") deformations of the metric, but unfortunately these deformations immediately disrupt some basic aspects of geometry and analysis, like rectifiability, differentiability, and curves of finite length. Here we discuss a (somewhat...

Gehring's lemma for metrics and higher integrability of the gradient for minimizers of noncoercive variational functionals

Bruno Franchi, Francesco Serra Cassano (1996)

Studia Mathematica

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We prove a higher integrability result - similar to Gehring's lemma - for the metric space associated with a family of Lipschitz continuous vector fields by means of sub-unit curves. Applications are given to show the higher integrability of the gradient of minimizers of some noncoercive variational functionals.