共查询到20条相似文献,搜索用时 31 毫秒
1.
Young Ja Park 《Proceedings of the American Mathematical Society》2004,132(7):2075-2083
A logarithmic Sobolev trace inequality is derived. Bounds on the best constant for this inequality from above and below are investigated using the sharp Sobolev inequality and the sharp logarithmic Sobolev inequality.
2.
Yong-Hua Mao 《Journal of Mathematical Analysis and Applications》2008,338(2):1092-1099
A general Sobolev type inequality is introduced and studied for general symmetric forms by defining a new type of Cheeger's isoperimetric constant. Finally, concentration of measure for the Lp type logarithmic Sobolev inequality is presented. 相似文献
3.
Wei-Shyan Tai 《Proceedings of the American Mathematical Society》2001,129(3):699-711
In this paper a capacitary weak type inequality for Sobolev functions is established and is applied to reprove some well-known results concerning Lebesgue points, Taylor expansions in the -sense, and the Lusin type approximation of Sobolev functions.
4.
Chengjie Yu 《manuscripta mathematica》2010,132(3-4):295-306
In this article, we get a time-dependent Sobolev inequality along the Ricci flow in a more general situation than those in Zhang (A uniform Sobolev inequality under Ricci flow. Int Math Res Not IMRN 2007, no 17, Art ID rnm056, 17 pp), Ye (The logarithmic Sobolev inequality along the Ricci flow. arXiv:0707.2424v2) and Hsu (Uniform Sobolev inequalities for manifolds evolving by Ricci flow. arXiv:0708.0893v1) which also generalizes the results of them. As an application of the time-dependent Sobolev inequality, we get a growth of the ratio of non-collapsing along immortal solutions of Ricci flow. 相似文献
5.
J. Michael Pearson 《Proceedings of the American Mathematical Society》1997,125(11):3339-3345
A new logarithmic Sobolev inequality for the real line is obtained. The inequality is obtained by applying a differentiation argument to a sharp Sobolev inequality due to Nagy, and is rather that in structure.
6.
A reduction theorem is established, showing that any Sobolev inequality, involving arbitrary rearrangement-invariant norms with respect to the Gauss measure in Rn, is equivalent to a one-dimensional inequality, for a suitable Hardy-type operator, involving the same norms with respect to the standard Lebesgue measure on the unit interval. This result is exploited to provide a general characterization of optimal range and domain norms in Gaussian Sobolev inequalities. Applications to special instances yield optimal Gaussian Sobolev inequalities in Orlicz and Lorentz(-Zygmund) spaces, point out new phenomena, such as the existence of self-optimal spaces, and provide further insight into classical results. 相似文献
7.
Ivan Gentil 《Journal of Functional Analysis》2003,202(2):591-599
We prove a general optimal Lp-Euclidean logarithmic Sobolev inequality by using Prékopa-Leindler inequality and a special Hamilton-Jacobi equation. In particular we generalize the inequality proved by Del Pino and Dolbeault in (J. Funt. Anal.). 相似文献
8.
O. S. Rothaus 《Proceedings of the American Mathematical Society》1998,126(8):2309-2314
We show that many of the recent results on exponential integrability of Lip 1 functions, when a logarithmic Sobolev inequality holds, follow from more fundamental estimates of the growth of norms under the same hypotheses.
9.
Ivan Gentil 《Bulletin des Sciences Mathématiques》2002,126(6):507-524
Following the equivalence between logarithmic Sobolev inequality, hypercontractivity of the heat semigroup showed by Gross and hypercontractivity of Hamilton-Jacobi equations, we prove, like the Varopoulos theorem, the equivalence between Euclidean-type Sobolev inequality and an ultracontractive control of the Hamilton-Jacobi equations. We obtain also ultracontractive estimations under general Sobolev inequality which imply in the particular case of a probability measure, transportation inequalities. 相似文献
10.
In this paper we introduce and study a weakened form of logarithmic Sobolev inequalities in connection with various others
functional inequalities (weak Poincaré inequalities, general Beckner inequalities, etc.). We also discuss the quantitative
behaviour of relative entropy along a symmetric diffusion semi-group. In particular, we exhibit an example where Poincaré
inequality can not be used for deriving entropic convergence whence weak logarithmic Sobolev inequality ensures the result.
相似文献
11.
We prove the equivalence between a general logarithmic Sobolev inequality and the hypercontractivity of a Hamilton–Jacobi equation. We also recover that this property imply a transportation inequality established by [5]. These results provide a natural generalization of the work performed in [3]. To cite this article: I. Gentil, F. Malrieu, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 437–440. 相似文献
12.
Alexander I. Nazarov 《Journal of Global Optimization》2008,40(1-3):289-303
We describe recent results on attainability of sharp constants in the Sobolev inequality, the Sobolev–Poincaré inequality,
the Hardy–Sobolev inequality and related inequalities. This gives us the solvability of boundary value problems to critical
Emden–Fowler equations.
相似文献
13.
Error estimates for scattered data interpolation on spheres 总被引:5,自引:0,他引:5
We study Sobolev type estimates for the approximation order resulting from using strictly positive definite kernels to do interpolation on the -sphere. The interpolation knots are scattered. Our approach partly follows the general theory of Golomb and Weinberger and related estimates. These error estimates are then based on series expansions of smooth functions in terms of spherical harmonics. The Markov inequality for spherical harmonics is essential to our analysis and is used in order to find lower bounds for certain sampling operators on spaces of spherical harmonics.
14.
Tony Lelièvre 《Journal of Functional Analysis》2009,256(7):2211-2221
We present a general criteria to prove that a probability measure satisfies a logarithmic Sobolev inequality, knowing that some of its marginals and associated conditional laws satisfy a logarithmic Sobolev inequality. This is a generalization of a result by N. Grunewald et al. [N. Grunewald, F. Otto, C. Villani, M.G. Westdickenberg, A two-scale approach to logarithmic Sobolev inequalities and the hydrodynamic limit, Ann. Inst. H. Poincaré Probab. Statist., in press]. 相似文献
15.
16.
Liming Wu 《Probability Theory and Related Fields》2000,118(3):427-438
By means of the martingale representation, we establish a new modified logarithmic Sobolev inequality, which covers the previous
modified logarithmic Sobolev inequalities of Bobkov-Ledoux and the L
1-logarithmic Sobolev inequality obtained in our previous work. From it we derive several sharp deviation inequalities of Talagrand's
type, by following the powerful Herbst method developed recently by Ledoux and al. Moreover this new modified logarithmic
Sobolev inequality is transported on the discontinuous path space with respect to the law of a Lévy process.
Received: 16 June 1999 / Revised version: 13 March 2000 / Published online: 12 October 2000 相似文献
17.
Dario D. Monticelli 《Journal of Differential Equations》2009,247(7):1993-2026
For second order linear equations and inequalities which are degenerate elliptic but which possess a uniformly elliptic direction, we formulate and prove weak maximum principles which are compatible with a solvability theory in suitably weighted versions of L2-based Sobolev spaces. The operators are not necessarily in divergence form, have terms of lower order, and have low regularity assumptions on the coefficients. The needed weighted Sobolev spaces are, in general, anisotropic spaces defined by a non-negative continuous matrix weight. As preparation, we prove a Poincaré inequality with respect to such matrix weights and analyze the elementary properties of the weighted spaces. Comparisons to known results and examples of operators which are elliptic away from a hyperplane of arbitrary codimension are given. Finally, in the important special case of operators whose principal part is of Grushin type, we apply these results to obtain some spectral theory results such as the existence of a principal eigenvalue. 相似文献
18.
In this note, we prove the Stein–Weiss inequality on general homogeneous Lie groups. The obtained results extend previously known inequalities. Special properties of homogeneous norms play a key role in our proofs. Also, we give a simple proof of the Hardy–Littlewood–Sobolev inequality on general homogeneous Lie groups. 相似文献
19.
Tristan C. Collins 《Journal of Geometric Analysis》2014,24(3):1323-1336
In this paper we prove a uniform Sobolev inequality along the Sasaki–Ricci flow. In the process, we develop the theory of basic Lebesgue and Sobolev function spaces, and prove some general results about the decomposition of the heat kernel for a class of elliptic operators on a Sasaki manifold. 相似文献
20.
Michel Ledoux 《Comptes Rendus Mathematique》2005,340(4):301-304
We present a one-dimensional version of the functional form of the geometric Brunn–Minkowski inequality in free (non-commutative) probability theory. The proof relies on matrix approximation as used recently by Biane and Hiai et al. to establish free analogues of the logarithmic Sobolev and transportation cost inequalities for strictly convex potentials, that are recovered here from the Brunn–Minkowski inequality as in the classical case. The method is used to extend to the free setting the Otto–Villani theorem stating that the logarithmic Sobolev inequality implies the transportation cost inequality. To cite this article: M. Ledoux, C. R. Acad. Sci. Paris, Ser. I 340 (2005). 相似文献