Displaying similar documents to “How to get rid of one of the weights in a two-weight Poincaré inequality?”

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.

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...

On imbedding theorems for weighted anisotropic Sobolev spaces

Wojciech M. Zajączkowski (2002)

Applicationes Mathematicae

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Using the Il'in integral representation of functions, imbedding theorems for weighted anisotropic Sobolev spaces in 𝔼ⁿ are proved. By the weight we assume a power function of the distance from an (n-2)-dimensional subspace passing through the domain considered.

General Gagliardo Inequality and Applications to Weighted Sobolev Spaces

Antonio Avantaggiati, Paola Loreti (2009)

Bollettino dell'Unione Matematica Italiana

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In this paper we obtain a more general inequality with respect to a well known inequality due to Gagliardo (see [4], [5]). The inequality contained in [4], [5] has been extended to weighted spaces, obtained as cartesian product of measurable spaces. As application, we obtain a first order weighted Sobolev inequality. This generalize a previous result obtained in [2].