Post-Widder算子线性组合加Jacobi权的Lp同时逼近

给出了Post-Widder算子线性组合加Jacobi权的Lp同时逼近的正、逆定理和逼近阶的特征刻划．     

On Some Properties of Multiple Moduli of Continuity

For functions of several variables a property is established similar to the well-known result of S. B. Stechkin about the metric property of almost increasing functions. In the case of one variable the proof is easier than the known one.     

On Estimating Integral Moduli of Continuity of Functions of Several Variables in Terms of Fourier Coefficients

Inequalities are derived which enable one to estimate integral moduli of continuity of functions of several variables in terms of Fourier coefficients.     

On Jackson's Inequality for Generalized Moduli of Continuity

Mathematical Notes -     

大偏差与lp-值Wiener过程在H(o)lder范数下的泛函连续模

本文在Holder范数生成的强拓扑下,建立了l~2-值Wiener过程的大偏差公式,从而得到了l~2-值与l~p-值Wiener过程在Holder范数下的泛函连续模.     

大偏差与l~p-值Wiener过程在Hlder范数下的泛函连续模

本文在Holder范数生成的强拓扑下,建立了l~2-值Wiener过程的大偏差公式,从而得到了l~2-值与l~p-值Wiener过程在Holder范数下的泛函连续模.     

Distribution of Global Measures of Deviation Between the Empirical Distribution Function and Its Concave Majorant

We investigate the distribution of some global measures of deviation between the empirical distribution function and its least concave majorant. In the case that the underlying distribution has a strictly decreasing density, we prove asymptotic normality for several L _k -type distances. In the case of a uniform distribution, we also establish their limit distribution together with that of the supremum distance. It turns out that in the uniform case, the measures of deviation are of greater order and their limit distributions are different.     

On the Majorant Method for the Cauchy--Kovalevskaya Problem

We present a theory which allows us to justify the existence theorems and derive majorant estimates for solutions of the Cauchy problem for a countable system of partial differential equations. Our results also allow to estimate the maximum existence interval for a solution.     

On Certain Best Constants for Bernstein-Type Operators

We discuss the generalized version of a best-constant problem raised by Z. Li in a note which recently appeared in Journal of Approximation Theory. Some best constants for well known Bernstein-type operators are obtained.     

Weighted Least Squares Method for the Accelerated Failure Time Model with Auxiliary Covariates

This paper deals with the analysis of accelerated failure time model when the primary covariate is subject to missing. We assume that the true covariate is     

Functional Modulus of Continuity for Brownian Motion in Holder Norm

The author establishes a large deviation for κ-dimensional Brownian motion B in stronger topology, by which the functional modulus of continuity for B in Hoelder norm can be obtained.     

Jackson算子关于二阶连续模的最佳逼近常数

求了用Jackson算子Jn（f.,x）逼近函数f（x）（∈C2n）时关于二阶连续模的最佳逼近常数：及用阶数不超过n的三角多项式H对连续函数f（x）的最佳逼近En（f）,的上界估计：     

The Rate of Approximation by Rational Bernstein Functions in Terms of Second Order Moduli of Continuity

The aim of this note is to study the impact of the weight numbers in two concrete cases on the rate of approximation by rational Bernstein functions. The approximation is measured in terms of second order moduli of continuity. We consider also the case of rational Bernstein curves and the role of the weights to modify the shape of the curves.     

Properties of Convergence for a Class of Generalized $q$-Gamma Operators.

In this paper, a generalization of $q$-Gamma operators based on the concept of $q$-integer is introduced. We investigate the moments and central moments of the operators by computation, obtain a local approximation theorem and get the pointwise convergence rate theorem and also obtain a weighted approximation theorem. Finally, a Voronovskaya type asymptotic formula was given.     

多线性分数次积分迭代型交换子的加权不等式

研究了多线性分数次积分算子的迭代型交换子,给出了双权强型不等式的充分条件,即Fefferman -Phong型条件.对此迭代型交换子,还给出了Fefferman-Stein型加权不等式和Coifman型加权不等式.     

线性模型中加权混合估计相对于最小二乘估计的两种相对效率

本文提出了线性模型中加权混合估计相对于最小二乘估计的两种相对效率,并给出了这些相对效率的上下界.     

Weighted Estimates for the Maximal Commutator of Singular Integral Operator on Spaces of Homogeneous Type

Weighted estimates with general weights are established for the maximal operator associated with the commutator generated by singular integral operator and BMO function on spaces of homogeneous type, where the associated kernel satisfies the HSlder condition on the first variable and some condition which is fairly weaker than the Holder condition on the second variable.     

Approximation by <Emphasis Type="Italic">p</Emphasis>-Faber-Laurent Rational Functions in the Weighted Lebesgue Spaces

Let L C be a regular Jordan curve. In this work, the approximation properties of the p-Faber-Laurent rational series expansions in the weighted Lebesgue spaces L ^p(L, ) are studied. Under some restrictive conditions upon the weight functions the degree of this approximation by a kth integral modulus of continuity in L ^p(L, ) spaces is estimated.