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1.
本文对满足条件AH=A>0,1/2(B+BH)≥0的矩阵A,B,建立了四个行列式不等式.某些著名的行列式不等式和一些已知结用,均可作为其推论. 相似文献
2.
关于含有Stirling公式的双边不等式(英) 总被引:2,自引:1,他引:1
本文证明了有关n!的一个便于应用的双边不等式,它对一切自然数都成立,且当n变大时,上界不等式能给出误差界为O(n-3)的Stirling渐近公式,从一定意义上说,文中的上界不等式具有最优形式,因为其中的常数0.5已作了最佳选择.文末还给出了关于Catalan数的一个双边不等式. 相似文献
3.
本文考察不等式:tr(AB)m≤tr(AmBm),m=1,2,3,…,其中A,B为K阶方阵.证明了当A正定B对称幂等条件下上述不等式成立.还考察了A,B为非负矩阵时的情形 相似文献
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一类分层三角剖分下三次样条空间的维数 总被引:1,自引:0,他引:1
本文定义了平面单连通多边形域的一类较任意的三角剖分-分层三角剖分,并通过分析二元样条的积分协调条件,确定了分层三角剖分卜三次C1作条函数空间的维数. 相似文献
7.
设(?)是Rn中的Vitali族,0≤γ≤1,定义分数次极大算子如下:本文得到了上述分数次极大算子的加权弱型不等式和加权强型不等式. 相似文献
8.
设△*任何三角剖分△的HCT细分的三角剖分.本文建立了定义于△*上的二元样条函数空间Sr(3r)(△*)的维数公式.我们的证明方法同时给出了Sr(3r)(△*)的一组显示的基函数,并阐明基函数具有某种意义的局部最小支集 相似文献
9.
继[15].本中考虑了带不同权函数L2[-1,1]空间中的Bernstcin-Markov不等式,给出了其最佳常数;最后还得到相应的反向Bernstcin-Markov不等式. 相似文献
10.
关于单形空间角的准正弦概念及应用 总被引:1,自引:0,他引:1
建立了欧氏空间En中n维单形空间角的准正弦概念,并应用于高维正弦定理的改进、Steiner定理的高维推广及切点不等式的简化证明;又推出了有关单形的一些新不等式. 相似文献
11.
New sharp Lorentz–Sobolev inequalities are obtained by convexifying level sets in Lorentz integrals via the L
p
Minkowski problem. New L
p
isocapacitary and isoperimetric inequalities are proved for Lipschitz star bodies. It is shown that the sharp convex Lorentz–Sobolev
inequalities are analytic analogues of isocapacitary and isoperimetric inequalities. 相似文献
12.
Hardy-Sobolev type inequalities on the H-type group 总被引:1,自引:0,他引:1
Motivated by the idea of Badiale and Tarantello who have found Hardy-Sobolev inequalities on Rn, a class of Hardy-Sobolev type inequalities on H-type groups is proved via a new representation formula for functions. Extremal
functions realizing equality in the inequalities are discussed by refined Concentration-Compactness principles. Finally, some
sharp constants for Hardy type inequalities are given.
The project supported by National Natural Science Foundation of China, Grant No. 10371099. 相似文献
13.
Yong Hua Mao 《数学学报(英文版)》2009,25(12):2055-2064
Lp Poincare inequalities for general symmetric forms are established by new Cheeger's isoperimetric constants. Lp super-Poincare inequalities are introduced to describe the equivalent conditions for the Lp compact embedding, and the criteria via the new Cheeger's constants for those inequalities are presented. Finally, the concentration or the volume growth of measures for these inequalities are studied. 相似文献
14.
Gabriel Larotonda 《Journal of Functional Analysis》2008,255(11):3208-3228
In this paper we introduce a new technique for proving norm inequalities in operator ideals with a unitarily invariant norm. Among the well-known inequalities which can be proved with this technique are the Löwner-Heinz inequality, inequalities relating various operator means and the Corach-Porta-Recht inequality. We prove two general inequalities and from them we derive several inequalities by specialization, many of them new. We also show how some inequalities, known to be valid for matrices or bounded operators, can be extended with this technique to normed ideals in C∗-algebras, in particular to the noncommutative Lp-spaces of a semi-finite von Neumann algebra. 相似文献
15.
Zhichun Zhai 《Potential Analysis》2011,34(1):1-12
This note proves sharp affine Gagliardo–Nirenberg inequalities which are stronger than all known sharp Euclidean Gagliardo–Nirenberg inequalities and imply the affine L p -Sobolev inequalities. The logarithmic version of affine L p -Sobolev inequalities is verified. Moreover, an alternative proof of the affine Moser–Trudinger and Morrey–Sobolev inequalities is given. The main tools are the equimeasurability of rearrangements and the strengthened version of the classical Pólya–Szegö principle. 相似文献
16.
A. A. Ligun 《Mathematical Notes》1976,19(6):533-541
In this note inequalities between the norms of a spline and its derivatives in various Orlich spaces are obtained. These inequalities are analogs of the inequalities of L. V. Takov for trigonometrical polynomials and generalize S. N. Bernstein's inequalities. An inequality for monosplines which reduces to the best quadrature formula for the classes WrL1, where r=1, 2,..., is also obtained. For r=2, 4, 6, ... this result was obtained earlier by V. P. Motornyi.Translated from Matematicheskie Zametki, Vol. 19, No. 6, pp. 913–926, June, 1976. 相似文献
17.
Lu Xuguang 《逼近论及其应用》2000,16(3):10-31
Under the only assumption of the cone property for a given domain Ω⊂R n, it is proved that interpolation inequalities for intermediate derivatives of functions in the Sobolev spaces Wm,p (Ω) or even in some weighted Sobolve spaces W w m,p (Ω) still hold. That is, the usual additional restrictions that Ω is bounded or has the uniform cone property are both removed. The main tools used are polynomial inequalities, by which it is also obtained pointwise version interpolation inequalities for smooth and analytic functions. Such pointwise version inequalities give explicit decay estimates for derivatives at infinity in unbounded domains which have the cone property. As an application of the decay estimates, a previous result on radial basis function approximation of smooth functions is extended to the derivative-simultaneous approximation. 相似文献
18.
We discuss the higher dimensional Bonnesen-style inequalities.Though there are many Bonnesen-style inequalities for domains in the Euclidean plane R2 few results for general domain in R n(n ≥ 3) are known.The results obtained in this paper are for general domains,convex or non-convex,in Rn. 相似文献
19.
The main results of this paper concern sharp constants for the Moser‐Trudinger inequalities on spheres in complex space ?n. We derive Moser‐Trudinger inequalities for smooth functions and holomorphic functions with different sharp constants (see Theorem 1.1). The sharp Moser‐Trudinger inequalities under consideration involve the complex tangential gradients for the functions and thus we have shown here such inequalities in the CR setting. Though there is a close connection in spirit between inequalities proven here on complex spheres and those on the Heisenberg group for functions with compact support in any finite domain proven earlier by the same authors [17], derivation of the sharp constants for Moser‐Trudinger inequalities on complex spheres are more complicated and difficult to obtain than on the Heisenberg group. Variants of Moser‐Onofri‐type inequalities are also given on complex spheres as applications of our sharp inequalities (see Theorems 1.2 and 1.3). One of the key ingredients in deriving the main theorems is a sharp representation formula for functions on the complex spheres in terms of complex tangential gradients (see Theorem 1.4). © 2004 Wiley Periodicals, Inc. 相似文献
20.
R. G. Salakhudinov 《Russian Mathematics (Iz VUZ)》2010,54(8):48-56
Let G be a simply connected domain and let u(x,G) be its warping function. We prove that L p -norms of functions u and u ?1 are monotone with respect to the parameter p. This monotony also gives isoperimetric inequalities for norms that correspond to different values of the parameter p. The main result of this paper is a generalization of classical isoperimetric inequalities of St.Venant-Pólya and the Payne inequalities. 相似文献