共查询到20条相似文献,搜索用时 15 毫秒
1.
M.S. Moslehian 《Linear algebra and its applications》2009,430(4):1131-1987
We give an extension of Hua’s inequality in pre-Hilbert C∗-modules without using convexity or the classical Hua’s inequality. As a consequence, some known and new generalizations of this inequality are deduced. Providing a Jensen inequality in the content of Hilbert C∗-modules, another extension of Hua’s inequality is obtained. We also present an operator Hua’s inequality, which is equivalent to operator convexity of given continuous real function. 相似文献
2.
Estibalitz Durand-Cartagena Nageswari Shanmugalingam Alex Williams 《Mathematische Zeitschrift》2012,271(1-2):447-467
We point out some of the differences between the consequences of p-Poincaré inequality and that of ∞-Poincaré inequality in the setting of doubling metric measure spaces. Based on the geometric characterization of ∞-Poincaré inequality given in Durand-Cartagena et al. (Mich Math J 60, 2011), we obtain a geometric property implied by the support of a p-Poincaré inequality, and demonstrate by examples that an analogous geometric characterization for finite p is not possible. The examples we give are metric measure spaces which are doubling and support an ∞-Poincaré inequality, but support no finite p-Poincaré inequality. In particular, these examples show that one cannot expect a self-improving property for ∞-Poincaré inequality in the spirit of Keith–Zhong (Ann Math 167(2):575–599, 2008). We also show that the persistence of Poincaré inequality under measured Gromov–Hausdorff limits fails for ∞-Poincaré inequality. 相似文献
3.
Functional Inequalities for the Decay of Sub-Markov Semigroups 总被引:3,自引:0,他引:3
A general functional inequality is introduced to describe various decays of semigroups. Our main result generalizes the classical one on the equivalence of the L
2-exponential decay of a sub-Markov semigroup and the Poincaré inequality for the associated Dirichlet form. Conditions for the general inequality to hold are presented. The corresponding isoperimetric inequality is studied in the context of diffusion and jump processes. In particular, Cheeger's inequality for the principal eigenvalue is generalized. Moreover, our results are illustrated by examples of diffusion and jump processes. 相似文献
4.
《Quaestiones Mathematicae》2013,36(8):1031-1043
AbstractThe (p, q)-mixed geominimal surface areas are introduced. A special case of the new concept is the Lp geominimal surface area introduced by Lutwak. Related inequalities, such as a?ne isoperimetric inequality, monotonous inequality, cyclic inequality, and Brunn-Minkowski inequality, are established. These new inequalities strengthen some well-known inequalities related to the Lp geominimal surface area. 相似文献
5.
Feng-Yu Wang 《Journal of Functional Analysis》2002,194(2):288-310
As a continuation of [13] where a Poincaré-type inequality was introduced to study the essential spectrum on the L2-space of a probability measure, this paper provides a modification of this inequality so that the infimum of the essential spectrum is well described even if the reference measure is infinite. High-order eigenvalues as well as the corresponding semigroup are estimated by using this new inequality. Criteria of the inequality and estimates of the inequality constants are presented. Finally, some concrete examples are considered to illustrate the main results. In particular, estimates of high-order eigenvalues obtained in this paper are sharp as checked by two examples on the Euclidean space. 相似文献
6.
Guillermina Jasso 《The Journal of mathematical sociology》2018,42(4):186-204
ABSTRACTAre there things that ordinary people can do in their private lives to reduce economic inequality? And, if so, how would these things work? To be sure, there are macro societal mechanisms for reducing inequality. But are there micro mechanisms for reducing inequality? This article first examines inequality measures and behavioral models that produce inequality effects, identifying five sets of inequality mechanisms which lead to levers that ordinary people can use to reduce income inequality, and next discusses the levers, with special attention to their feasibility, ease of use, and side effects. The five levers highlight transfers, equal additions, negative assortative mating, wage schedules that reward multiple personal characteristics, and compensation procedures with voting rules, many voters, diversity of thought, and secret ballots. This work raises new questions for research, such as the sources of diversity of thought. 相似文献
7.
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.
8.
9.
The dimension-free Harnack inequality and uniform heat kernel upper/lower bounds are derived for a class of infinite-dimensional GEM processes, which was introduced in Feng and Wang (J. Appl. Probab. 44 938–949 2007) to simulate the two-parameter GEM distributions. In particular, the associated Dirichlet form satisfies the super log-Sobolev inequality which strengthens the log-Sobolev inequality derived in Feng and Wang (J. Appl. Probab. 44 938–949 2007). To prove the main results, explicit Harnack inequality and super Poincaré inequality are established for the one-dimensional Wright-Fisher diffusion processes. The main tool of the study is the coupling by change of measures. 相似文献
10.
By using a coupling method, an explicit log-Harnack inequality with local geometry quantities is established for (sub-Markovian) diffusion semigroups on a Riemannian manifold (possibly with boundary). This inequality as well as the consequent L2-gradient inequality, are proved to be equivalent to the pointwise curvature lower bound condition together with the convexity or absence of the boundary. Some applications of the log-Harnack inequality are also introduced. 相似文献
11.
Anthony Carbery 《Proceedings of the American Mathematical Society》2004,132(11):3141-3152
We prove a multilinear inequality which in the bilinear case reduces to the Cauchy-Schwarz inequality. The inequality is combinatorial in nature and is closely related to one established by Katz and Tao in their work on dimensions of Kakeya sets. Although the inequality is ``elementary" in essence, the proof given is genuinely analytical insofar as limiting procedures are employed. Extensive remarks are made to place the inequality in context.
12.
The aim of this paper is to study the relationship among Minty vector variational-like inequality problem, Stampacchia vector variational-like inequality problem and vector optimization problem involving (G, α)-invex functions. Furthermore, we establish equivalence among the solutions of weak formulations of Minty vector variational-like inequality problem, Stampacchia vector variational-like inequality problem and weak efficient solution of vector optimization problem under the assumption of (G, α)-invex functions. Examples are provided to elucidate our results. 相似文献
13.
An affine rearrangement inequality is established which strengthens and implies the recently obtained affine Pólya–Szeg? symmetrization
principle for functions on
\mathbb Rn{\mathbb R^n} . Several applications of this new inequality are derived. In particular, a sharp affine logarithmic Sobolev inequality is
established which is stronger than its classical Euclidean counterpart. 相似文献
14.
Tran Dan Thu 《Annals of Combinatorics》2013,17(4):755-763
The LYMinequality (Lubell, Yamamoto, Meshalkin) is a generalization of Sperner’s theorem for antichains. Kleitman and Harper independently proved that the LYM inequality and the normalized matching property (or local LYM inequality) are equivalent. Many contributions have been proposed to sharpen the LYM inequality. Noticeably, Ahlswede and Zhang lifted the LYM inequality to an identity, called the AZ identity. Thus, one expects that the same sharpening of the local LYM inequality is equivalent to the AZ identity. In this paper, we introduce a local LYM identity which sharpens the local LYM inequality and prove that it is equivalent to the AZ identity. The local LYM identity shows local relationships between components in the AZ identity. 相似文献
15.
C.-S. Lin 《Proceedings of the American Mathematical Society》2001,129(3):855-859
Two of the most useful inequality formulas for bounded linear operators on a Hilbert space are the Löwner-Heinz and Reid's inequalities. The first inequality was generalized by Furuta (so called the Furuta inequality in the literature). We shall generalize the second one and obtain its related results. It is shown that these two generalized fundamental inequalities are all equivalent to one another.
16.
The Harnack inequality established in Röckner and Wang (J Funct Anal 203:237–261, 2003) for generalized Mehler semigroup is improved and generalized. As applications, the log-Harnack inequality, the strong Feller property, the hyper-bounded property, and some heat kernel inequalities are presented for a class of O-U type semigroups with jump. These inequalities and semigroup properties are indeed equivalent, and thus sharp, for the Gaussian case. As an application of the log-Harnack inequality, the HWI inequality is established for the Gaussian case. Perturbations with linear growth are also investigated. 相似文献
17.
In this paper we derive a simple inequality involving expectations of convex functions and the notion of G-majorization. The result extends a similar inequality of Marshall and Proschan (1965), J. Math. Anal. Applic. Useful applications of the more general inequality are presented. 相似文献
18.
Regarding the generalizations of the Bessel inequality in Hilbert spaces which are due to Bombieri and Boas–Bellman, we obtain a version of the Bessel inequality and some generalizations of this inequality in the framework of Hilbert C *-modules. 相似文献
19.
The two-level pressure projection stabilized finite element methods for Navier-Stokes equations with nonlinear slip boundary conditions are investigated in this paper, whose variational formulation is the Navier-Stokes type variational inequality problem of the second kind. Based on the P1-P1 triangular element and using the pressure projection stabilized finite element method, we solve a small Navier-Stokes type variational inequality problem on the coarse mesh with mesh size H and solve a large Stokes type variational inequality problem for simple iteration or a large Oseen type variational inequality problem for Oseen iteration on the fine mesh with mesh size h. The error analysis obtained in this paper shows that if h=O(H2), the two-level stabilized methods have the same convergence orders as the usual one-level stabilized finite element methods, which is only solving a large Navier-Stokes type variational inequality problem on the fine mesh. Finally, numerical results are given to verify the theoretical analysis. 相似文献
20.
Jeffrey D. Vaaler 《Monatshefte für Mathematik》2008,88(1):323-343
We prove an upper bound for the Mahler measure of the Wronskian of a collection of N linearly independent polynomials with complex coefficients. If the coefficients of the polynomials are algebraic numbers
we obtain an inequality for the absolute Weil heights of the roots of the polynomials. This later inequality is analogous
to the abc inequality for polynomials, and also has applications to Diophantine problems. 相似文献