ON BONNESEN-STYLE SYMMETRIC MIXED ISOHOMOTHETIC INEQUALITY IN R^2

In this paper,we investigate the translative containment measure for a convex domain K_i to contain,or to be contained in the homothetic copy of another convex domain tK_j(t≥0).Via the formulas of translative Blaschke and Poincare in integral formula,we obtain a Bonnesen-style symmetric mixed isohomothetic inequality.The Bonnesen-style symmetric mixed isohomothetic inequality obtained is known as Bonnesen-style inequality if one of the domains is a disc.As a direct consequence,we attain an inequality which strengthen the result proved by Bonnesen,Blaschke and Flanders.Furthermore,by the containment measure and Blaschke’s rolling theorem,we obtain the reverse Bonnesen-style symmetric mixed isohomothetic inequalities.These inequalities are the analogues of the known Bottema’s result in 1933.

On Reverses of the Blaschke-Santalo Inequality for Convex Bodies

Reisner proved a reverse of the Blaschke-Santal5 inequality for zonoid bodies, Bourgain and Milman showed another reverse of the Blaschke-Santal5 inequality for centered convex bodies. In this paper, two reverses of the Blaschke-Santal5 inequality for convex bodies are given by the Petty projection inequality and above two reverses. Further, using above methods, we also obtain two analogues of the Petty＇s conjecture for projection bodies, respectively.

On Reverses of the Lp-petty Projection Inequality

Lutwak, Yang and Zhang established the Lp-petty projection inequality. In this paper, the several reverses of the Lp-petty projection inequality are shown.

Extension of reverse Hilbert-type inequality with some parameters

By introducing some parameters and estimating the weight function,we obtain an extension of reverse Hilbert-type inequality with the best constant factor.As applications,we build its equivalent forms and some particular results.

Some Results on Reverses of Cauchy-Schwarz Inequality in Inner Product Spaces

Some new reverses of the Cauchy-Schwarz inequality in inner product spaces are presented in this paper. As an application of the main result, a formula for error estimate concerning Cauchy-Schwarz’s inequality is provided. The results obtained in the paper complement and improve some recent work about this topic.

Bonnesen-style Isoperimetric Inequalities of an n-simplex

In this paper,by the theory of geometric inequalities,some new Bonnesenstyle isoperimetric inequalities of n-dimensional simplex are proved.In several cases,these inequalities imply characterizations of regular simplex.

Inequalities relating to L_p-version of Petty's conjectured projection inequality

Petty＇s conjectured projection inequality is a famous open problem in the theory of convex bodies. In this paper, it is shown that an inequality relating to Lp-version of the Petty＇s conjectured projection inequality is developed by using the notions of the Lp-mixed volume and the Lp-dual mixed volume, the relation of the Lp-projection body and the geometric body Г-pK, the Bourgain-Milman inequality and the Lp-Bnsemann-Petty inequality. In addition, for each origin-symmetric convex body, by applying the Jensen inequality and the monotonicity of the geometric body Г-pK, the reverses of Lp-version of the Petty＇s conjectured projection inequality and the Lp-Petty projection inequality are given, respectively.

The Reverse Holder Classes in Martingale Setting

In martingale setting, it has been shown thatA p weights can be factorized in terms ofA 1 weights. This factorization benefits many problems very much. In this paper, the new class of RH∞ plays the same role for RH s , which makes the reverse H?lder inequalities hold with exponents>1, that the classA 1 does forA p class. Therefore, the Jones' factorization theorem forA p weights was extended to include some information about the reverse H?lder classes. And it is the most convenient object in weight theory indeed. Key words martingale space - minimal function - weight inequality - reverse H?lder class CLC number O 221. 4 Foundation item: Supported by the National Natural Science Foundation of China (19771063)Biography: Zuo Hong-liang (1976-), male, Ph. D candidate, research direction: martingale theory.

一类非齐次核有界积分算子的反问题

基于有界算子的本质之一:当原象集有界时象集一定有界,提出算子有界的反问题,即当算子T的象集有界时,如何判断其原象集有界.先引入算子反向有界的概念,再利用权函数方法和实分析技巧,讨论积分算子反向有界的等价参数条件,并给出反向有界积分算子的构造定理.最后给出一些特例.

THE WEIGHTED KATO SQUARE ROOT PROBLEMOF ELLIPTIC OPERATORS HAVING A BMOANTI-SYMMETRICPART

Let n≥2 and let L be a second-order elliptic operator of divergence form with coefficients consisting of both an elliptic symmetric part and a BMO anti-symmetric part in ℝ^(n).In this article,we consider the weighted Kato square root problem for L.More precisely,we prove that the square root L^(1/2)satisfies the weighted L^(p)estimates||L^(1/2)(f)||L_(ω)^p(R^(n))≤C||■f||L_(ω)^p(R^(n);R^(n))for any p∈(1,∞)andω∈Ap(ℝ^(n))(the class of Muckenhoupt weights),and that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,2+ε)andω∈Ap(ℝ^(n))∩RH_(2+ε/p),(R^(n))(the class of reverse Hölder weights),whereε∈(0,∞)is a constant depending only on n and the operator L,and where(2+ε/p)'denotes the Hölder conjugate exponent of 2+ε/p.Moreover,for any given q∈(2,∞),we give a sufficient condition to obtain that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,q)andω∈A_(p)(R^(n))∩pRH_(q/p),(R^(n)).As an application,we prove that when the coefficient matrix A that appears in L satisfies the small BMO condition,the Riesz transform∇L^(−1/2)is bounded on L_(ω)^(p)(ℝ^(n))for any given p∈(1,∞)andω∈Ap(ℝ^(n)).Furthermore,applications to the weighted L^(2)-regularity problem with the Dirichlet or the Neumann boundary condition are also given.

逆弱鞅的一类概率不等式

给出逆弱鞅的Chow型极大值不等式和极小值不等式,利用Chow型极大值不等式得到了逆弱鞅的一类Doob型不等式,给出逆弱鞅的一类矩不等式.

逆弱鞅函数的一类Marshall型极大值概率不等式

逆弱下鞅是比鞅序列更为广泛的一类相依随机变量序列.本文利用一般随机变量的H9lder不等式和逆弱下鞅函数的Doob型极大值概率不等式,给出了逆弱下鞅函数{g(S_n),n≥1}在不同条件下的一类Marshall型极大值不等式,这里g是R上单调增的下凸函数.

On Reverses of the L_p-Busemann-Petty Centroid Inequality and Its Applications

In this paper,the reverse forms of the L p-Busemann-Petty centroid inequality are shown. As the applications of the reverse forms,we obtain the reverse forms of the L p-centroid-affine inequality and an upper bound of the isotropic constant for convex bodies.

Brascamp-Lieb inequality for positive double John basis and its reverse

In this paper, we establish the Brascamp-Lieb inequality for positive double John basis and its reverse. As their applications, we estimate the upper and lower bounds for the volume product of two unit balls with the given norms. Moreover, the Loomis-Whitney inequality for positive double John basis is obtained.

Some integral inequalities on time scales

In this article, we study the reverse HSlder type inequality and HSlder inequality in two dimensional case on time scales. We also obtain many integral inequalities by using HSlder inequalities on time scales which give Hardy＇s inequalities as spacial cases.

The Reverse Petty Projection Inequality

It is proved that if K is an origin-symmetric convex body in R^2 and Π^*K is the polar projection body of K,then the volumes of K and Π^*K satisfy the inequality V(K)V(Π^*K)≥2 with equality if K is a parallelogram.

New Developments on Operator Reverse AM-GM Inequality for Positive Linear Maps

In this research article,we shall give some reverse Arithmetic-Geometric mean inequalities for unital positive linear maps on Hilbert space operators under some different conditions.Our results are sharper and more precise as compared to some recent published results.Moreover,we shall present refinements of the Lin conjecture.

Reverse Bonnesen style inequalities in a surface X_∈~2 of constant curvature

We investigate the isoperimetric deficit upper bound, that is, the reverse Bonnesen style inequality for the convex domain in a surface X2 of constant curvature ε via the containment measure of a convex domain to contain another convex domain in integral geometry. We obtain some reverse Bonnesen style inequalities that extend the known Bottema＇s result in the Euclidean plane E2.

Some Bonnesen-style Inequalities for Higher Dimensions

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 Rn （n ≥ 3） are known. The results obtained in this paper are for general domains, convex or non-convex, in Rn.

矩阵乘积的加权最小二乘广义逆的反序律研究

加权广义逆是矩阵理论与应用中不可或缺的一部分,它在线性偏微分方程、多元统计分析、线性控制理论等领域有着广泛的应用.本文利用广义Schur补的极大极小秩这一方法研究了一些矩阵乘积的加权广义逆的反序律,给出了矩阵乘积的加权广义逆的反序律A_(3){1,3M_(3)}A_(2){1,3M_(2)}A_(1){1,3M_(1)}■(A_(1)A_(2)A_(3)){1,3M_(1)} 和 A_(3){1, 4M_(4)}A_(2){1, 4M_(3)}A_(1){1, 4M_(2)}■(A_(1)A_(2)A_(3)){1,4M_(4)}成立的充分必要条件.