GENERALIZED ROSENTHAL'S INEQUALITY FOR BANACH-SPACE-VALUED MARTINGALES

A generalized Rosenthal＇s inequality for Banach-space-valued martingales is proved, which extends the corresponding results in the previous literatures and characterizes the p-uniform smoothness and q-uniform convexity of the underlying Banach space. As an application of this inequality, the strong law of large numbers for Banach-space-valued martingales is also given.

向量值多线性奇异积分算子的加权Sharp不等式

利用不等式、原子分解性质研究了向量值多线性算子,证明了某些向量值多线性奇异积分算子的一个加权Sharp不等式,并利用此不等式得到了该向量值多线性算子的加权L^(p)型不等式和L log L型不等式。

Hadamard流形的子流形上的一些p-调和形式的消灭定理

本文研究了Hadamard流形N的完备浸入子流形M上的一些p-调和形式的消灭定理.首先,假设M满足加权庞加莱不等式且具有平坦法丛,N具有纯曲率张量且(l,n-l)-曲率不小于-kρ(0≤k≤4/p^(2)),2≤l≤n-2.如果总曲率足够小,我们得到了p-调和l-形式的消灭定理,推广了Wang-Chao-Wu-Lv在2018年的结果.其次,假设N是一个截面曲率满足-k^(2)≤K_(N)≤0的Hadamard流形,如果总曲率足够小且拉普拉斯的第一特征值满足某个下界,我们得到了p-调和1-形式的消灭定理,推广了Dung-Seo在2015年的结果.

The Oscillation Inequality of Harmonic Functions on Post Critically Finite Self-Similar Sets

In this paper we establish the oscillation inequality of harmonic functions and HOlder estimate of the functions in the domain of the Laplacian on connected post critically finite （p.c.f.） self-similar sets.

THE OPIAL INEQUALITY IN R^N

This paper discusses the minimal eigenvalue lambda (1)(p,q,Omega) and its best estimate of the following nonlinear eigenvalue problem -Delta (p)u = lambda \u \ (q-2)u, u \ (partial derivative Omega) = 0. Where Omega is a bounded smooth domain in R-N, Delta (p) is the p-laplace operator, p greater than or equal to 2, q is an element of [p, Np/N-p). [p, NP). By this result, the famous Opial inequality in R-N are deduced.

Vanishing Theorems on Smooth Metric Measure Spaces with a Weighted p-Poincare Inequality

This paper deals with vanishing results for Lf^2 harmonic p-forms on complete metric measure spaces with a weighted p-Poincare inequality.Some results are without curvature assumptions for 1■p■n-1 and the others are with assumptions on lower bound of the m-Bakry-Emery Ricci curvature for p=1.These are weighted version for the corresponding results of the present author(J.Math.Anal.Appl.,2020,490).

Hàjek-Rèniy Type Inequality for Banach Space Valued Martingales and Its Applications

In this paper,we establish the Hàjek-Rèniy type inequality for Banach space valued martingales generalizing the recent results of Tómcs and L'ibor [1].Then p-uniformly smoothable Banach space is characterized in terms of the Hàjek-Rèniy type inequality for Banach space valued martingales.Those results generalize the recent results of Gan Shixin [2].

Davis's Inequalities for Two-Parameter Banach Space Valued Strong Martingales and Geometrical Properties of Banach Spaces

In this paper we investigated theL 1 norm inequalities of theP square and the maximal functions of two-parameterB-valued strong martingales, which can be applied to characterizep-smoothness andq-convexity of Banach spaces.

Two Optimal Inequalities Related to the Sándor-Yang Type Mean and One-parameter Mean

In this paper, we establish two optimal the double inequalities for Sandor- Yang type mean and one-parameter mean.

Some Inequalities of Hermite-Hadamard Type for Functions Whose 3rd Derivatives Are <i>P</i>-Convex

In the paper, the authors establish some new Hermite-Hadamard type inequalities for functions whose 3rd derivatives are P-convex.

Pólya-Szeg不等式及积分不等式的证法改进

研究了文[1]中Polya-Szego不等式及推广了的积分不等式的繁琐程度,从而构造性的给出了这两个不等式的简洁证明.

TRANSPORTATION INEQUALITIES FOR WEAKLY DEPENDENT SEQUENCES

In [3], they gave necessary and sufficient condition for T 1 C and then as applications T 1 C for weakly dependent sequences was established. In this note, based on Gozlan-L′eonard characterization for W 1 H -inequalities, we extends this result to W 1 H inequalities.

凸函数的若干个(p,q)-积分不等式

(p,q)-微积分是q-微积分的推广,在数学和物理的许多领域有着广泛的应用。利用(p,q)-积分、(p,q)-导数和Jensen不等式,对多元连续凸函数的(p,q)-Hermite-Hadamard不等式进行推广和加细,得到了若干个新的(p,q)-积分不等式。

SOME INEQUALITIES FOR POLYNOMIALS SATISFYING p(z)=z^n p(1/z)

Let p(z)=be a polynomial degree n and let Then accord-ing to Bernstein's inequality ||p'||<n||p||.It is a well known open problem to obtain inequality analogous to Bernstein's inequality for the class IIn of polynomials satisfying p(z)≡znp(1/z)Here we obtain an inequality analogous to Bernstein's inequality for a subclass of IIn Our results include several of the known results as special cases.

Coefficient Inequalities for p-Valent Functions

In the present paper, the authors introduce a new subclass of p-valent analytic functions with complex order defined on the open unit disk U={z:z∈C and |z|<1} and obtain coefficient inequalities for the functions in these class. Application of these results for the functions defined by the convolution are also obtained.

广义L_(p)-混合弦长积分的Brunn-Minkowski型不等式与逆循环不等式

研究凸几何分析中星体的广义L_(p)-混合弦长积分,建立关于广义L_(p)-混合弦长积分的两类Brunn-Minkowski型不等式和一类逆循环不等式.

L_(p)-Minkowski问题周期解的存在性

L_(p)-Minkowski问题是凸几何分析L_(p)-Brunn-Minkowski理论的核心,其实质是分析给定测度是否为凸体的L_(p)表面积测度问题.这个问题可以简化为二阶微分方程的周期解的存在性,L_(p)-Minkowski问题中周期解的存在性问题如下u″+u=h(t)/u^(ρ),其中h>0是连续的周期函数,常数ρ=1-p.利用了二阶微分方程周期解存在的充分条件,通过建立的一个方程的周期解的存在性判据,再利用Sobolev inequality证明了这个二阶微分方程周期解的存在性,得到在一定条件下周期解存在,这个方法在一定程度上扩大p的取值范围.最后给出一个例子,验证文中所得到的主要结果的可行性.

修正二元Gauss-Weierstrass算子线性组合在L_(p)(R^(2)+)空间中的逼近

借助K-泛函、广义Minkowski不等式、极大函数的定义及其性质,给出修正二元Gauss-Weierstrass算子线性组合在L_(p)(R^(2)+)空间中的逼近定理,并对此定理进行了证明.

一类含有p次幂的Volterra-Fredholm型非线性迭代积分不等式

研究了一类含有p次幂的Volterra-Fredholm型迭代积分不等式.利用变量替换、放大方法、微分、积分和逆函数等不等式技巧给出了不等式中未知函数的估计,推广了相应的结果.为了说明结果的有效性,用所得结果给出了一类Volterra-Fredholm型积分方程解的估计.

P-凸函数及其性质

给出P-凸函数的定义及其性质,将一个有关凸函数的命题推广到P-凸函数情形,并指出赵海清等人关于该命题的证明过程是错误的.