关于新型Hilbert不等式的积分形式

本文利用分析的方法及不等式理论，建立了两个新型Hilbert不等式的积分形式，获得了一些新结果，推广了某些相关的结果．     

关于广义Hilbert双重级数不等式

本文建立了两个新型的广义Hilbert双重级数不等式.     

类似Hilbert不等式的一些新不等式的推广

本文推广了 Pachpatte在文 [1 ]中给出的类似 Hilbert不等式的一些新不等式 .     

关于Polya-Szeg不等式

本文给出两个改进的不等式,使改进后的每一个新的不等式均含有Polay-Szego两个不等式改进在内．     

关于Hilbert积分不等式新的改进和推广

本文通过引入一些常数，运用一些分析技巧和Young不等式，给出了Hilbert积分不等式的一些新的改进和推广。     

一个逆向Hilbert型不等式的推广及其应用

引入独立参数A及应用改进的Euler-Maclaurin求和公式以估算权系数,给出了—个具有最佳常数因子的逆向Hilbert型不等式的推广．作为应用,考虑了它的等价形式．     

参量化的Hilbert不等式

通过引入一些参数及估算权系数,给出一个推广的具有最佳常数因子的Hilbert重级数不等式,它联系着β函数．作为应用,考虑了它的等价形式及一些特殊结果．     

关于Polya-Szegoe不等式

本文给出两个改进的不等式,使改进后的每一个新的不等式均含有Polay-Szeg（o）两个不等式改进在内.     

Schur不等式和Hoelder不等式及其应用

Schur不等式和Hoelder不等式是两个重要的不等式，本讲我们介绍Schur不等式和Hoelder不等式及其应用．     

一个对偶的Hardy-Hilbert不等式及其推广

本文给出一个对偶的具有最佳常数因子的Hardy-Hilbert不等式,它是Hilbert不等式的具有(p,q)-参数形式的新推广,还考虑了它的更为推广的单参数形式及一个等价不等式。     

On Variance and Covariance for Bounded Linear Operators

In this paper we initiate a study of covariance and variance for two operators on a Hilbert space, proving that the c-v (covariance-variance) inequality holds, which is equivalent to the Cauchy-Schwarz inequality. As for applications of the c-v inequality we prove uniformly the Bernstein-type inequalities and equalities, and show the generalized Heinz-Kato-Furuta-type inequalities and equalities, from which a generalization and sharpening of Reid's inequality is obtained. We show that every operator can be expressed as a p-hyponormal-type, and a hyponormal-type operator. Finally, some new characterizations of the Furuta inequality are given. Received April 9, 2000, Revised July 20, 2000, Accepted August 8, 2000     

Inequalities of Reid type and Furuta

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.

     

On a mixed Kernel Hilbert‐type integral inequality and its operator expressions with norm

By using some real analysis techniques, we study the structural characteristics of a multi‐parameter Hilbert‐type integral inequality with the hybrid kernel and obtain some equivalent conditions for this inequality. We also consider the operator expression of the equivalent inequalities. The conclusions not only integrate some results of references but also find some new Hilbert‐type integral inequalities with simple form by choosing suitable parameter values.     

Two new forms of half-discrete Hilbert inequality

In this paper, we introduce two new forms of the half-discrete Hilbert inequality. The first form is a sharper form of the half-discrete Hilbert inequality and is related to Hardy inequality. In the second one, we give a differential form of this inequality.     

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．     

A Buzano type inequality for two Hermitian forms and applications

A Buzano type inequality for two nonnegative Hermitian forms is obtained. Applications to inequalities for norm and numerical radius of bounded linear operators in complex Hilbert spaces are given.     

A bilinear inequality

We establish an inequality for symmetric bilinear forms involving both the norm and the inner product of vectors. We use the inequality to convert known inequalities in real Hilbert spaces such as classical Hilbert's inequality to sharper inequalities.     

On new generalizations of the Hilbert integral inequality

Some new generalizations of the Hilbert integral inequality by introducing real functions ?(x) and ψ(x). The results of this paper reduce to those of the corresponding inequalities proved by Gao [Mingzhe Gao, On Hilbert's integral inequality, Math. Appl. 11 (3) (1998) 32-35]. Some applications are considered.     

一个含多参数且-4齐次核的Hilbert型积分不等式

以Hilbert不等式为代表的双线型不等式是分析学的重要不等式.应用权函数方法,引入多个参数,建立了一个新的具有最佳常数因子的-4齐次核的双线型不等式.作为应用,导出其等价形式及一些特殊结果.     

On some generalizations of the Hilbert–Hardy type discrete inequalities

New Hilbert-type discrete inequalities are presented by using new techniques in proof. By specializing the weight coefficient functions in the hypothesis and the parameters, we obtain many special cases which include, in particular, the discrete inequality derived by Hilbert and Hardy. Many improvements and generalizations of known results are given in this paper.