DECOMPOSITION OF BV FUNCTIONS IN CARNOT-CARATHÉODORY SPACES

The aim of this paper is to get the decomposition of distributional derivatives of functions with bounded variation in the framework of Carnot-Carathéodory spaces (C-C spaces in brievity) in which the vector fields are of Carnot type. For this purpose the approximate continuity of BV functions is discussed first, then approximate differentials of L¹ functions are defined in the case that vector fields are of Carnot type and finally the decomposition Xu = ∇u · Lⁿ + X^sи is proved, where и ∈ BVx(Ω) and ∇u denotes the approximate differential of u.     

Heisenberg群H~n上的有界变差函数

本文有四个目标:一是研究了H-Caccioppoli集的几何性质;二是证明了H~n上有界变差函数u的跳跃集J_u是H-Rectifiable并刻画不连续集S_u和跳跃集J_u的特征;三是证明了u在Ω上几乎处处近似可微并研究u的逐点行为;最后还证明了D_Hu作为Radon测度能分解成三部分,即D_Hu=L_u·~(2n+1)+2w_(2n-1)/w_(2n+1)(u~+-u~-)v_uS_d~(Q-1)J_u+_H~cu,其中L_u ∈ R~(2n)是u的近似微分,u~+,u~-,v_u分别是u在跳跃点的近似上、下极限和跳跃方向。     

关于CARATH(E)ODORY函数的充分条件和应用

本文研究了Carathéodory函数.利用微分从属的方法,得到了单位圆盘内Carathéodory函数的某些充分条件.结果改进了文献[1,2,4,5]的结论.     

DIFFERENTIABILITY OF CONVEX FUNCTIONS AND ASPLUND SPACES

ＤＩＦＦＥＲＥＮＴＩＡＢＩＬＩＴＹＯＦＣＯＮＶＥＸＦＵＮＣＴＩＯＮＳＡＮＤＡＳＰＬＵＮＤＳＰＡＣＥＳＣｈｅｎｇＬｉｚｉｎ（程立新）ＺｈａｎｇＦｅｎｇ（张风）（Ｍａｔｈ．Ｓｅｃｔｉｏｎ，Ｄｅｐｔ．ｏｆＰｕｂｌｉｃＣｏｕｒｓｅｓ，ＪｉａｎｇｈａｎｒＰｅｔ...     

EXISTENCE OF GENERALIZED WEAKLY SOLUTIONS OF DIFFERENTIAL EQUATIONS IN PRODUCT SPACES

In this paper, by using Lyapunov function and weak noncompactness conditions, we give an existence theorem of generalized weakly solutions of Cauchy problem of differential equations in product spaces.     

THE EXISTENCE OF RADIAL LIMITS OF ANALYTIC FUNCTIONS IN BANACH SPACES

Let X be a comPlex Banach space and let D be the open unit disc in the complex plane.We shall denote by H"(D, X) the Banach space consisting of all uniformly bounded X-vaued analytic functions defined on D equipped with the norm llflloo = suP lIf(z)Il. Az eDcomplex Banach space X is said to have the analytic Radon-NikOdym property if eachelemellt f E Hoo(D,X) has radial limits almost everywhere on the torus T = {e": 0 E[0, 2x]} (see [1]), this means that for almost all 0 C [0,27l, 9W…     

SOME DOUBLE SEQUENCE SPACES OF FUZZY NUMBERS DEFINED BY ORLICZ FUNCTIONS

In this article, we introduce some double sequence spaces of fuzzy real numbers defined by Orlicz function, study some of their properties like solidness, symmetricity, completeness etc, and prove some inclusion results.     

析函数的(FN)-代数中的闭理想问题

本文讨论了解析函数的(FN)-代数A0P中的闭理想问题,利用射影加权系给出了一个闭理想成为A0P中的补子空间的判别准则.     

矢值Banach序列空间ss(E)的端点和强暴露点

本文讨论赋序列范数的矢值Banach序列空间ss(E)的几何性质．利用SS和SS(E)的关系刻化了ss(E)的端点和强暴露点，给出了它们的判据，并推广了lp(E)的结果．     

DIFFERENTIABILITY OF CONVEX FUNCTIONS ON SUBLINEAR TOPOLOGICAL SPACES AND VARIATIONAL PRINCIPLES IN LOCALLY CONVEX SPACES

This paper presents a type of variational principles for real valued w lower semicon-tinuous functions on certain subsets in duals of locally convex spaces, and resolve a problem concerning differentiability of convex functions on general Banach spaces. They are done through discussing differentiability of convex functions on nonlinear topological spaces and convexification of nonconvex functions on topological linear spaces.     

EXISTENCE OF WEAK SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS IN BANACH SPACES

0 IntroductionRecently, the study of ordinary differential equations in a Banach spacehas been developed extensively by using the strong topology, see [2],13],[4]. Atpresent, however, there is no reference or paper which systematically studiesweak solutions of the Cauchy problem of ordinary differential equation in theweak topology. In references [l],15],[7] and [8], several results of weak solutionsare proved. In this paper, we shall give the other results of weak solutions,some of which are…     

SOME BOUNDARY INCREASING PROPERTIES OF HARMONIC FUNCTIONS IN LIPSCHITZ DOMAIN

The object of this paper is to study the non-tangential increasing properties of positiveharmonic function u in Lipschitz domain by means of Martin representation theory. A necessaryand sufficient condition of the control of growth of u near any fixed boundary point is obtained.It is shown that the non-tangential increasing degree of u near a boundary point is exactlythe local degree of its representation measure with respect to the harmonic measure. Someexamples are given.     

AREA FUNCTIONS ON HARDY SPACES ASSOCIATED TO SCHR(O)DINGER OPERATORS

In this paper, the author gives a characterization of atomic Hardy spacesassociated to Schrodinger operators by using area functions, and hence gets the dual spacesof atomic Hardy spaces.     

A REMARK ON DUALITY FOR THE SUM OF CONVEX FUNCTIONS IN GENERAL BANACH SPACES

§１．ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＥｂｅａｒｅａｌＢａｎａｃｈｓｐａｃｅ，ｎｏｔｎｅｃｅｓａｒｉｌｙｒｅｆｌｅｘｉｖｅ．ＬｅｔΦ，Ψ：Ｅ→］－∞，∞］ｂｅｔｗｏｌｏｗｅｒｓｅｍｉｃｏｎｔｉｎｕｏｕｓｃｏｎｖｅｘｆｕｎｃｔｉｏｎｓ．Ｗｅｄｅｎｏｔｅ...     

DERIVATIVES OF HARMONIC MIXED NORM AND BLOCH-TYPE SPACES IN THE UNIT BALL OF Rn

Let H(B) be the set of all harmonic functions f on the unit ball B of Rn. For 0 < p, q ≤ ∞ and a normal weight φ, the mixed norm space Hp,q, φ(B) consists of all functions f in H(B) for which the mixed norm p,q, φ < ∞. In this article, we obtain some characterizations in terms of radial, tangential, and partial derivative norms in Hp,q, φ(B). The parallel results for the Bloch-type space are also obtained. As an application, the analogous problems for polyharmonic functions are discussed.     

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．     

代数多项式和指数型整函数在Besov空间中的逼近

用Ｋ－泛函定义了一类Ｂｅｓｏｖ空间,并分别用ｎ阶代数多项式及指数为σ的整函数的最佳逼近阶给出了其特征的刻画。     

APPROXIMATION OF A KIND OF NEVAI-DURRMEYER OPERATORS IN Lpw SPACES

The present paper introduces a kind of Nevai-Durrmeyer operators which can be used to approximate functions in Lpw spaces with the weight w(x)=1√1-x2 and the approximate rate is also estimated.     

TWO ENTIRE FUNCTIONS SHARING FOUR SMALL FUNCTIONS IN THE SENSE OF (E-)k)(β, f)= (E-)k)(β,g)

This paper proves a result that if two entire functions f(z) and g(z) share foursmall functions aj (z) (j = 1,2, 3, 4) in the sense of Ek) (aj, f) = Ek)(aj, g), (j = 1, 2, 3, 4)(k ≥ 11), then there exists f(z) = g(z).