Heisenberg型群上一类精确Hardy型不等式和Hardy-Sobolev型不等式及应用(英文)

本文在Heisenberg型群上建立了一类精确的Hardy型不等式。采用的技巧是逼近及正则化的方法。进一步利用这个结果,本文建立了一类精确的Hardy-Sobolev型不等式。这两个结果包括了已有的相关结果。作为应用,讨论了一类具有Hardy位势的非线性算子的正定性与下无界性。     

离散型Carlson's不等式的一些推广及改进

In this paper, we consider Carlson type inequalities and discuss their possible improvement. First, we obtain two different types of generalizations of discrete Carlson's inequality by using the Hlder inequality and the method of real analysis, then we combine the obtained results with a summation formula of infinite series and some Mathieu type inequalities to establish some improvements of discrete Carlson's inequality and some Carlson type inequalities which are equivalent to the Mathieu type inequalities. Finally, we prove an integral inequality that enables us to deduce an improvement of the Nagy-Hardy-Carlson inequality.     

Generalization and sharpness of the power means inequality and their applications

In this paper, we generalize and sharpen the power means inequality by using the theory of majorization and the analytic techniques. Our results unify some optimal versions of the power means inequality. As application, a well-known conjectured inequality proposed by Janous et al. is proven. Furthermore, these results are used for studying a class of geometric inequalities for simplex, from which, some interesting inequalities including the refined Euler inequality and the reversed Finsler-Hadwiger type inequality are obtained.     

On general Bernstein and Nikol’ski type inequalities

The goal of this paper is to establish the relations between general Bernstein and Nikol’ski type inequalities under some weak conditions. From these relations some known classical inequalities are implied. Also, a family of functions equipped with Bernstein type inequality which satisfies Nikol’ski type inequality is found.     

Moment inequalities for the partial sums of random variables

This paper discusses the conditions under which Rosenthal type inequality is obtained from M-Z-B type inequality. And M-Z-B type inequality is proved for a wide class of random variables. Hence Rosenthal type inequalities for some classes of random variables are obtained.     

高阶可微函数Ostrowski型不等式

研究了一类n阶可微函数,利用其n阶导数上、下界以及Cruis不等式,给出了n阶可微函数Ostrowski型不等式,从而推广二阶可微函数Ostrowski型不等式.     

二次可微函数的Ostrowski型不等式

研究了一类二次可微函数,利用二阶导数的上界和下界,给出了二次可微函数的O strow sk i型不等式,同时也推广了经典的中点不等式和梯形不等式.     

Functional Inequalities for the Decay of Sub-Markov Semigroups

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.     

An extension of Harnack type determinantal inequality

We revisit and comment on the Harnack type determinantal inequality for contractive matrices obtained by Tung in the nineteen sixties and give an extension of the inequality involving multiple positive semidefinite matrices .     

General Sobolev type inequalities for symmetric forms

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.     

Hardy-Hilbert型积分不等式的一个推广及其应用

本文讨论带参数的Hardy-Hilbert型积分不等式.利用改进了的Hlder不等式对它进行了推广,作为其应用,给出了Hardy-Littlewood不等式的推广.     

关于双曲函数的Huygens型不等式及应用

给出了关于双曲函数的Huygens型不等式,并得到了双曲函数的Wilker型不等式的加强.定义了一类新的Seiffert型平均,给出两个有关不等式.     

关于反余弦函数的Shafer-Fink型不等式

改进了Carlson不等式,得到了关于反余弦函数的Shafer-Fink型不等式.     

关于hilbert－ingham不等式和它的应用

本文给出（ｉ）ｈｉｌｂｅｒｔ不等式和ｈｉｌｂｅｒｔ－ｉｎｇｈａｍ不等式一些有意义的共同改进；（ｉｉ）一些ｆｅｊｅｒ－ｒｉｅｓｚ型不等式的改进和（ｉｉｉ）ｈａｒｄｙ不等式的改进．     

Criteria for Super-and Weak-Poincaré Inequalities of Ergodic Birth-Death Processes

Criteria for the super-Poincaré inequality and the weak-Poincaré inequality about ergodic birth-death processes are presented. Our work further completes ten criteria for birth-death processes presented in Table 1.4 (p. 15) of Prof. Mu-Fa Chen's book "Eigenvalues, Inequalities and Ergodic Theory" (Springer, London, 2005). As a byproduct, we conclude that only ergodic birth-death processes on finite state space satisfy the Nash inequality with index 0 ν≤ 2.     

Beckner Inequality on Finite- and Infinite-Dimensional Manifolds

By using the dimension-free Harnack inequality, the coupling method, and Bakry-Emery's argument, some explicit lower bounds are presented for the constant of the Beckner type inequality on compact manifolds. As applications, the Beckner inequality and the transportation cost inequality are established for a class of continuous spin systems. In particular, some results in [1, 2] are generalized.     

Stability criteria for linear periodic Hamiltonian systems

In this paper, we obtain new stability criteria for linear periodic Hamiltonian systems. A Lyapunov type inequality is established. Our results improve the existing works in the literature.     

基于扰动结点的Lagrange插值算子逼近的 Steckin-Marchaud型不等式

建立了基于扰动超球Jacobi结点的Marcinkiewicz zygmund不等式并借助一种新的K泛函给出了基于扰动超球Jacobi结点的积分型Lagrange插值算子逼近的Steckin Marchaud型不等式.     

A Dvoretzky–Kiefer–Wolfowitz type inequality for the Kaplan–Meier estimator

We prove a new exponential inequality for the Kaplan–Meier estimator of a distribution function in a right censored data model. This inequality is of the same type as the Dvoretzky–Kiefer–Wolfowitz inequality for the empirical distribution function in the non-censored case. Our approach is based on Duhamel equation which allows to use empirical process theory.     

Some results related to permanental inequalities

The FKG inequality and associated inequalities have been extensively studied in the literature. The FKG inequality has been extended to a 2m-function inequality which relates to some interesting permanental inequalities. In this paper, we prove some related inequalities and also give a simple alternative proof of the 2m-function inequality. Our proofs use tools of majorization theory and are thus based on a completely different approach than the usual one.