On equivalence of super log Sobolev and Nash type inequalities

Marco Biroli; Patrick Maheux

Displaying similar documents to “On equivalence of super log Sobolev and Nash type inequalities”

Extrapolation of Sobolev imbeddings.

M. Krbec (1997)

Collectanea Mathematica

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We survey recent results on limiting imbeddings [sic] of Sobolev spaces, particularly, those concerning weakening of assumptions on integrability of derivatives, considering spaces with dominating mixed derivatives and the case of weighted spaces.

Logarithmic Sobolev Inequalities and Concentration of Measure for Convex Functions and Polynomial Chaoses

Radosław Adamczak (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

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Sharp constants for Moser-type inequalities concerning embeddings into Zygmund spaces

Robert Černý (2012)

Commentationes Mathematicae Universitatis Carolinae

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Let $n \geq 2$ and $Ω \subset ℝ^{n}$ be a bounded set. We give a Moser-type inequality for an embedding of the Orlicz-Sobolev space $W_{0} L^{Φ} (Ω)$ , where the Young function $Φ$ behaves like $t^{n} {log}^{α} (t)$ , $α < n - 1$ , for $t$ large, into the Zygmund space $Z_{0}^{\frac{n - 1 - α}{n}} (Ω)$ . We also study the same problem for the embedding of the generalized Lorentz-Sobolev space $W_{0}^{m} L^{\frac{n}{m}, q} {log}^{α} L (Ω)$ , $m < n$ , $q \in (1, \infty]$ , $α < \frac{1}{q^{'}}$ , embedded into the Zygmund space $Z_{0}^{\frac{1}{q^{'}} - α} (Ω)$ .

Direct and Reverse Gagliardo-Nirenberg Inequalities from Logarithmic Sobolev Inequalities

Matteo Bonforte, Gabriele Grillo (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

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We investigate the connection between certain logarithmic Sobolev inequalities and generalizations of Gagliardo-Nirenberg inequalities. A similar connection holds between reverse logarithmic Sobolev inequalities and a new class of reverse Gagliardo-Nirenberg inequalities.

Large deviation principles for Markov processes via phi-Sobolev inequalities.

Wu, Liming, Yao, Nian (2008)

Electronic Communications in Probability [electronic only]

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An embedding theorem for Sobolev type functions with gradients in a Lorentz space

Alireza Ranjbar-Motlagh (2009)

Studia Mathematica

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The purpose of this paper is to prove an embedding theorem for Sobolev type functions whose gradients are in a Lorentz space, in the framework of abstract metric-measure spaces. We then apply this theorem to prove absolute continuity and differentiability of such functions.

Modified log-Sobolev inequalities for convex functions on the real line. Sufficient conditions

Radosław Adamczak, Michał Strzelecki (2015)

Studia Mathematica

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We provide a mild sufficient condition for a probability measure on the real line to satisfy a modified log-Sobolev inequality for convex functions, interpolating between the classical log-Sobolev inequality and a Bobkov-Ledoux type inequality. As a consequence we obtain dimension-free two-level concentration results for convex functions of independent random variables with sufficiently regular tail decay. We also provide a link between modified log-Sobolev...

Continuity properties of functions from Orlicz-Sobolev spaces and embedding theorems

Andrea Cianchi (1996)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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From the Prékopa-Leindler inequality to modified logarithmic Sobolev inequality

Ivan Gentil (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

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We develop in this paper an improvement of the method given by S. Bobkov and M. Ledoux in [BL00]. Using the Prékopa-Leindler inequality, we prove a modified logarithmic Sobolev inequality adapted for all measures on $ℝ^{n}$ , with a strictly convex and super-linear potential. This inequality implies modified logarithmic Sobolev inequality, developed in [GGM05, GGM07], for all uniformly strictly convex potential as well as the Euclidean logarithmic Sobolev inequality.

Sobolev and isoperimetric inequalities for Dirichlet forms on homogeneous spaces

Marco Biroli, Umberto Mosco (1995)

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

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We prove local embeddings of Sobolev and Morrey type for Dirichlet forms on spaces of homogeneous type. Our results apply to some general classes of selfadjoint subelliptic operators as well as to Dirichlet operators on certain self-similar fractals, like the Sierpinski gasket. We also define intrinsic BV spaces and perimeters and prove related isoperimetric inequalities.