Rearrangement Free Method for Hardy-Littlewood-Sobolev Inequalities on $\mathbb{S}^n$

For conformal Hardy-Littlewood-Sobolev(HLS) inequalities [22] and reversed conformal HLS inequalities [8] on $\mathbb{S}^n,$ a new proof is given for the attainability of their sharp constants. Classical methods used in [22] and [8] depends on rearrangement inequalities. Here, we use the subcritical approach to construct the extremal sequence and circumvent the blow-up phenomenon by renormalization method. The merit of the method is that it does not rely on rearrangement inequalities.     

三个矩阵秩不等式中等号成立的充分必要条件

研究了线性代数课程教学中三个矩阵秩的不等式,得到了不等式等号成立的充分必要条件.     

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.     

Hlder不等式和Minkowski不等式的推广

本文利用变分方法对多个变元的不含变元导数的Holder不等式和Minkowski不等式进行了推广．此种方法的主要意义不在于证明传统的不等式，而在于发现新的不等式．     

索伯列夫嵌入不等式的证明

We consider the problem about the space embedded by tile space and the embed-ding inequality. With the Holder inequality and interpolation inequality, we give the proof of the space embedding theorem and the space holder embedding theorem.     

一个-4齐次核的Hardy-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。近代利用权函数方法,该类不等式的推广应用研究得到深入的发展。本文应用权函数的方法,建立了一个具有最佳常数因子的-4齐次核的双线型不等式,作为应用,导出其等价的不等式。     

三阶可微函数的若干不等式

通过建立与Bullen不等式有关的积分恒等式,利用Halder不等式、Grüss不等式、Chebychev不等式,给出三阶可微函数的一些不等式.     

幂幺矩阵的充要条件

研究幂幺矩阵的充要条件,利用矩阵的秩和齐次线性方程组解空间的维数.将m=2时幂幺矩阵的充要条件推广到一般幂幺矩阵的充要条件,得出了幂幺矩阵可对角化的结果,并将幂幺矩阵的充要条件平行地推广到幂幺线性变换.     

加权Fan Ky不等式及其加细

本文简证了加权Ｋｙ Ｆａｎ不等式，给出了两种加细形式。     

Necessary and Sufficient Conditions for Solving Infinite-Dimensional Linear Inequalities

The existence of a feasible solution to a system of infinite-dimensional linear inequalities is characterized by a topological generalization of the Farkas Condition. If this result is specialized to a finite-dimensional vector space with finite positive cone, then a geometric proof of the classic Minkowski-Farkas Lemma is obtained. A dual version leads to an infinite-dimensional extension of the Theorem of the Alternative.     

On Approximation of Function Classes in Lorentz Spaces with Anisotropic Norm

In this paper, Lorentz space of functions of several variables and Besov＇s class are considered. We establish an exact approximation order of Besov＇s class by partial sums of Fourier＇s series for multiple trigonometric system.     

Lipschitz条件下的加权梯形不等式和中点不等式

利用与一阶导数有关的积分恒等式,并通过引入参数求最值,在一 阶导函数满足Lipschitz条件的情况下,给出加权梯形不等式和中点不等式.     

一个积分不等式的证明及应用

利用概率技巧或H?lder不等式,可证∫Cxnf（x）dx ＞∫Cxf（x）dx ,其中 f （x）为连续型随机变量X的在其可能取值的区间C上的密度函数。     

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.     

An Improved Hardy's Inequality

In this paper we shall extend Hardy's inequality associated with Fourier transform to the strip n(2-p) ≤ σ < n+p(N +1) where N = [n(1/p-1)], the greatest integer not exceeding n(1/p−1).     

E—matrices and Several Necessary and Sufficient Conditions

AER-x.,Aiscalledanonnegative(nonPositive)matrixifau>O(a,jO(aiirtO),markedA>O(AO(i#j),auO,wecallp(A)=max{IA,l,lA,l'.-.,lAnl},(whereA,,A2,..',A"areeigenva1ueofA)asspectralradiusofA.LemmalIfAe7'.,thenareanonnegativesquarematrxBandapositivenumberksuchthatA=B-kI(whereIistheidentitymatrixofordern).ProofLetbti=…     

AN IMPROVED HARDY＇S INEQUALITY

In this paper we shall extend Hardy’s inequality associated with Fourier trans-form to the strip n(2?p)≤σ相似文献   

Necessary and Sufficient Conditions for Mcshane’s Identity and Variations

Greg McShane introduced a remarkable identity for lengths of simple closed geodesics on the once punctured torus with a complete, finite volume hyperbolic structure. Bowditch later generalized this and gave sufficient conditions for the identity to hold for general type-preserving representations of a free group on two generators Γ to SL(2,C), this was further generalized by the authors to obtain sufficient conditions for a generalized McShane’s identity to hold for arbitrary (not necessarily type-preserving) non-reducible representations in Tan et al. (Submitted). Here we extend the above by giving necessary and sufficient conditions for the generalized McShane identity to hold (Akiyoshi, Miyachi and Sakuma had proved it for type-preserving representations). We also give a version of Bowditch’s variation of McShane’s identity to once-punctured torus bundles, in the case where the monodromy is generated by a reducible element, and provide necessary and sufficient conditions for the variations to hold.     

拟共形映射Lp -可积指数的上确界

设 f 是R²中单位圆 B²上的K -拟共形映射, 该文证明了 $\sup_{0相似文献   

Two Suficient and Necesary Conditions for Quasidisks

ＴｗｏＳｕｆｉｃｉｅｎｔａｎｄＮｅｃｅｓａｒｙＣｏｎｄｉｔｉｏｎｓｆｏｒＱｕａｓｉｄｉｓｋｓ＊）ＣｈｕＹｕｍｉｎｇ（褚玉明）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＨｕｎａｎＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｃｈａｎｇｓｈａ，４１００８２）...