HARNACK EXTENSION FOR THE HENSTOCK INTEGRAL IN THE EUCLIDEAN SPACE

Classical integration theory as Presented by Saks contains basically one proof, namely, the proof by category argument (see,for example,[‘4 ;p, 253] or [1；p, 47]). A key step in the proof is the use of Harnack extension for the Henstock inregral. In this note,we shall reformulate the Harnack extension so that it is real-line independent.     

AREA INTEGRAL FUNCTIONS FOR SECTORIAL OPERATORS ON L^p SPACES

Area integral functions are introduced for sectorial operators on Lp-spaces. We establish the equivalence between the square and area integral functions for sectorial operators on Lpspaces. This follows that the results of Cowling, Doust, McIntosh, Yagi, and Le Merdy on H∞functional calculus of sectorial operators on Lp-spaces hold true when the square functions are replaced by the area integral functions.     

具有齐性核的Marcinkiewicz积分在Herz型Hardy空间的有界性

本文讨论了具有齐性核的Marcinkiewicz积分μΩ在Herz型Hardy空间的有界性,证明了μΩ是从HKqα,p(Rn)到Kqα,p(Rn)有界的.     

带小波函数的Cauchy主值积分的数值计算

1 引言 众所周知,小波方法在信号处理和图像处理方面发挥了举世瞩目的成就。近年来人们研究小波方法在数值分析方面的应用。期望在数值求解微分方程和积分方程方面发挥良好的作用。本文研究带有小波函数的Cauchy主值积分 的数值计算方法,其中Φ(x)是紧支撑的尺度函数。这是数值求解积分方程的核心问题之一。 1.l 多分辩分析 空间L~2(R)中的一个多分辩分析是这样的闭子空间列{V_j},它满足下列条件 1) 2) 3) 4)存在尺度函数,使构成V_o的Riesz基,从而也存在序列使满足双尺度方程     

Clifiord分析中双正则函数及调和函数在平面上的积分表示

本文研究了取值在Clifiord代数上双正则函数及调和函数在超复平面上积分表示的问题.利用构造核函数的方法,获得了双正则函数及调和函数在超复平面上的积分表示公式,这些结果推广了Clifiord分析中正则函数在超复平面上的积分表示公式.     

一类带有变量核的积分算子在Herz型Hardy空间的有界性

本文研究了带有变量核的奇异积分与分数次积分算子.当核函数满足一类Dini型条件时,证明了 这类算子从Herz型Hardy空间到Herz空间的有界性.     

非倍测度条件下由Marcinkiewicz积分与RBMO函数生成的交换子在Herz空间中的有界性

本文研究了非倍测度条件下的一类由Marcinkiewica积分与RBMO函数生成交换子的有界性.通过Marcinkiewica积分及该交换子在Lebesgue空间中的有界性,得到了此交换子在Herz空间中的有界性.     

SINGULAR INTEGRAL OPERATORS IN L~2 SPACES ASSOCIATED WITH THE GENERALIZED JACOBI WEIGHTS

In this paper, a kind of new definitions of singular integral operators in the weighted L2 space with the generalized Jacobi weights are given, then the boundedness in the weighted L2 space, the relationships between these operators and the classic singular integral operators are proved. For the convenience in the later use, similar results in the L2 space with Jacobi weights are given.     

BOUNDEDNESS OF GENERALIZED MARCINKIEWICZ INTEGRAL ON THE H~p-SOBOLEV SPACES

§ 1　IntroductionIn this paper,we consider the following general Marcinkiewicz integral:μΩ,αf (x) =∫∞0 ∫|x- y|≤ tΩ (x -y)| x -y| n- 1 f(y) dy2 dtt3+2α1 2 (1 .1 )for all f∈ S(Rn) ,α≥ 0 ,andΩ is a distribution kernel.Whenα=0 ,it is the classicalMacinkiewicz integral operator many mathematicians have studied.There are a lot ofreferences about the topic that you can find.Here we take a simple list of some results ofthis topic.In 1 958,Stein[8] firstproved that ifΩ∈ Lipα(Sn- 1…     

INTERIOR ESTIMATES IN MORREY SPACES FOR SOLUTIONS OF ELLIPTIC EQUATIONS AND WEIGHTED BOUNDEDNESS FOR COMMUTATORS OF SINGULAR INTEGRAL OPERATORS

It is proved that, for the nondivergence elliptic equations ∑in, j=1 aijuxixj = f,if f belongs to the generalized Morrey spaces Lp,ψ(ω), then uxixj ∈ Lp,ψ(ω), where u is the W2,p-solution of the equations. In order to obtain this, the author first establish the weighted boundedness for the commutators of some singular integral operators on Lp,ψ (ω).     

THE BOUNDEDNESS FOR A CLASS OF ROUGH FRACTIONAL INTEGRAL OPERATORS ON VARIABLE EXPONENT LEBESGUE SPACES

In this paper,we will discuss the behavior of a class of rough fractional integral operators on variable exponent Lebesgue spaces,and establish their boundedness from L p 1 (·) (R n) to L p 2 (·) (R n).     

带粗糙核的奇异积分交换子的有界性

本文研究了带粗糙核的奇异积分算子与BMO函数生成的交换子的有界性问题.利用原子分解的方法,获得了带粗糙核的奇异积分交换子TΩb在Lp空间、Hardy空间、弱Hardy空间上的有界性结果,推广了交换子Tb在各类函数空间上有界性的结果.     

GLOBAL APPROXIMATION FOR A CLASS OF GENERALIZED MIXED EXPONENTIAL TYPE INTEGRAL OPERATORS IN POLYNOMIAL WEIGHT SPACES

It is shown that a class of generalized mixed exponential type integral operatos on direct theorem of approximation and inverse theorem of approximation hold in CN(I).     

Hardy空间上一类带可变核的积分算子

本文给出了一类带可变核的奇异积分算子的（Hp,Lp）有界性及分数次积分算子的（Hp,Lq）有界性（0相似文献   

代数体函数涉及重值的Borel点

研究了单位圆内代数体函数涉及重值的Borel点的存在性,利用型函数统一证明了单位圆内无穷级,有限正级和部分零级代数体函数存在涉及重值的Borel点,并对有限正级的代数体函数得到两个必要条件.     

B值随机变量序列的局部收敛定理

本文的目的是研究B值随机变量序列的局部收敛定理。作为推论，得到了一类B值鞅差序列的极限定理和若干经典的独立随机变量序列的极限定理。     

Banach空间中Volterra非线性积分方程的Carathéodory解

本文在相当弱的条件下研究Ｂａｎａｃｈ空间中Ｖｏｌｔｅｒｒａ非线性积分方程的Ｃａｒａｔｈｅｏｄｏｒｙ解的存在性,证明方法简洁且与现有文献不同．     

带Hilbert核奇异积分方程解的稳定性

本文在Ｃｈｅｂｙｓｈｅｖ模下讨论了带Ｈｉｌｂｅｒｔ核奇异积分方程解的稳定性及其稳定性条件．证明了扰动方程的可解性及原方程的解对于已知函数的连续依赖性．     

圆周上带希尔伯特核的柯西奇异积分方程的数值解(英文)

本文研究了圆周上带希尔伯特核的柯西奇异积分的复合梯型公式.利用连续的分片线性函数逼近被积函数,得到积分公式的误差估计;然后用积分公式构造求解对应奇异积分方程的两种格式;最后给出数值实验验证理论分析结果.     

THE -PROBLEM FOR HOLOMORPHIC (0,2)-FORMS ON PSEUDOCONVEX DOMAINS IN SEPARABLE HILBERT SPACES AND D.F.N. SPACES

This paper shows that the -problem for holomorphic (0, 2)-forms on Hilbert spaces is solv able on pseudoconvex open subsets. By using this result, the authors investigate the existence of the solution of the -equation for holomorphic (0, 2)-forms on pseudoconvex domains in D.F.N. spaces.