Displaying similar documents to “A capacity approach to the Poincaré inequality and Sobolev imbeddings in variable exponent Sobolev spaces.”

An optimal endpoint trace embedding

Andrea Cianchi, Luboš Pick (2010)

Annales de l’institut Fourier

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We find an optimal Sobolev-type space on n all of whose functions admit a trace on subspaces of n of given dimension. A corresponding trace embedding theorem with sharp range is established.

Analytic and Geometric Logarithmic Sobolev Inequalities

Michel Ledoux (2011)

Journées Équations aux dérivées partielles

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We survey analytic and geometric proofs of classical logarithmic Sobolev inequalities for Gaussian and more general strictly log-concave probability measures. Developments of the last decade link the two approaches through heat kernel and Hamilton-Jacobi equations, inequalities in convex geometry and mass transportation.

Sharp embeddings of Besov spaces with logarithmic smoothness.

Petr Gurka, Bohumir Opic (2005)

Revista Matemática Complutense

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We prove sharp embeddings of Besov spaces B with the classical smoothness σ and a logarithmic smoothness α into Lorentz-Zygmund spaces. Our results extend those with α = 0, which have been proved by D. E. Edmunds and H. Triebel. On page 88 of their paper (Math. Nachr. 207 (1999), 79-92) they have written: ?Nevertheless a direct proof, avoiding the machinery of function spaces, would be desirable.? In our paper we give such a proof even in a more general context. We cover...