Logarithmic Sobolev Inequality and Exponential Convergence of a Markovian Semigroup in the Zygmund Space [PDF]
Entropy, 2018 We investigate the exponential convergence of a Markovian semigroup in the Zygmund space under the assumption of logarithmic Sobolev inequality. We show that the convergence rate is greater than the logarithmic Sobolev constant.
Ichiro Shigekawa
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The Pólya-Szegö Principle and the Anisotropic Convex Lorentz-Sobolev Inequality [PDF]
The Scientific World Journal, 2014 An anisotropic convex Lorentz-Sobolev inequality is established, which extends Ludwig, Xiao, and Zhang’s result to any norm from Euclidean norm, and the geometric analogue of this inequality is given.
Shuai Liu, Binwu He
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On three-dimensional Hall-magnetohydrodynamic equations with partial dissipation
Boundary Value Problems, 2022 In this paper, we address the Hall-MHD equations with partial dissipation. Applying some important inequalities (such as the logarithmic Sobolev inequality using BMO space, bilinear estimates in BMO space, Young’s inequality, cancellation property ...
Baoying Du
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Sharp Hardy-Sobolev Inequalities with General Weights and Remainder Terms
Journal of Inequalities and Applications, 2009 We consider a class of sharp Hardy-Sobolev inequality, where the weights are functions of the distance from a surface. It is proved that the Hardy-Sobolev inequality can be successively improved by adding to the right-hand side a lower-order term with ...
Yaotian Shen, Zhihui Chen
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Evaluation of the One-Dimensional Lp Sobolev Type Inequality
Mathematics, 2020 This study applies the extended L 2 Sobolev type inequality to the L p Sobolev type inequality using Hölder’s inequality. The sharp constant and best function of the L p Sobolev type inequality are found using a Green ...
Kazuo Takemura, Yoshinori Kametaka
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Interpolation inequalities in generalized Orlicz-Sobolev spaces and applications
Open Mathematics, 2023 Let m∈Nm\in {\mathbb{N}} and be a generalized Orlicz function. We obtained some interpolation inequalities for derivatives in generalized Orlicz-Sobolev spaces Wm,φ(Rn){W}^{m,\varphi }\left({{\mathbb{R}}}^{n}).
Wu Ruimin, Wang Songbai
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Lupaş-type inequality and applications to Markov-type inequalities in weighted Sobolev spaces
Bulletin of Mathematical Sciences, 2021 Weighted Sobolev spaces play a main role in the study of Sobolev orthogonal polynomials. In particular, analytic properties of such polynomials have been extensively studied, mainly focused on their asymptotic behavior and the location of their zeros. On
Francisco Marcellán +1 more
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From the Pr\'ekopa-Leindler inequality to modified logarithmic Sobolev inequality [PDF]
, 2007 We develop in this paper an improvement of the method given by S. Bobkov and M. Ledoux. Using the Pr\'ekopa-Leindler inequality, we prove a modified logarithmic Sobolev inequality adapted for all measures on $\dR^n$, with a strictly convex and super ...
Gentil, Ivan
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On the best constant of Hardy-Sobolev Inequalities [PDF]
, 2009 We obtain the sharp constant for the Hardy-Sobolev inequality involving the distance to the origin. This inequality is equivalent to a limiting Caffarelli-Kohn-Nirenberg inequality.
Adimurthi +2 more
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Hypercontractivity for perturbed diffusion semigroups [PDF]
, 2005 $\mu$ being a nonnegative measure satisfying some log-Sobolev inequality, we give conditions on F for the measure $\nu=e^{-2F} \mu$ to also satisfy some log-Sobolev inequality.
Cattiaux, Patrick
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