齐型空间上的指数平方类的刻画与应用

本文在齐型空间(X, d,μ)上建立与经典二进平方函数相联系的指数平方类的三个等价刻画,即指数平方可积性、好λ不等式及二进平方函数的Lp下界最佳估计.该工作推广了著名的Rn上ChangWilson-Wolff定理.作为应用,本文建立了非负Ricci曲率Riemann流形上与Laplace-Beltrami算子相联系的平方函数的L~p下界最佳估计.     

加权解析Lipschitz空间的等价范数

该文研究单位圆盘上加权解析Lipschitz空间的等价范数。作者首先推广文献［3］中的结果，给出了加权解析Lipschitz函数的p Garsia模刻画，然后用高阶导数刻画了加权解 析Lipschitz函数，并给出了它的Bergman Carleson测度特征。最后，还得到了加权解析Lipschitz函数类似于BMO指数衰减的John Nirenberg定理。     

g函数,弱基g函数和空间的度量化

函数刻画广义度量空间，最早可追溯至Heath和Hodel的工作. 近些年来，Nagat a和一些拓扑学者利用g函数系统地研究了度量化问题. 该文引入弱基g函数的概念，利用它给出拓扑空间度量化的一些等价刻画, 推广了前人的相关工作. 证明了拓扑空间X可以度量化，当且仅当X有弱基g函数满足条件(1)和(7).     

弱基g-函数在度量化中的应用

本文引入弱基g-函数的概念，利用它给出拓扑空间度量化的一些等价刻画，证明了拓扑空间X可以度量化，当且仅当X有弱基g-函数满足(s)和(g2)(或(ks)和g1)条件，另外，本文还给出了J．Nagata两个定理的简单证明。     

C~n上Fock空间之正交补空间上的对偶Toeplitz算子的紧性

讨论C~m上Fock空间之正交补空间上以平方可积函数为符号的对偶Toeplitz算子,并给出其有界性与紧性的等价判别条件.     

关于局部极小值点为整体极小值点的函数的一点注记

本引进了一种广义严格拟凸函数的定义,给出了它的一个刻画,证明 了局部极小值点为整体极小值点的函数与本定义的广义严格拟凸函数的等价性。     

学习理论中核函数逼近的Jackson型不等式（英文）

从微分算子角度理解核函数空间,借助经典Fourier变换研究核函数逼近问题.应用Fourier乘子算子和算子半群定义了一种光滑模,证明其与一种基于微分算子的K-泛函的等价性,由此给出了刻画核函数逼近收敛性的Jackson不等式.进一步证明,如果微分算子为Riesz势算子或Bessel势算子,逼近的收敛性可以转化为卷积算子逼近.特别地,给出了再生核Hilbert空间逼近的一种上界估计.     

Bloch函数到BMOA空间的距离

本文利用高阶导数形式给出了Bloch函数到BMOA空间的距离刻画.这些结论推广了由Peter Jones和赵如汉等人所得到的一阶导数形式的距离公式.作为应用,我们给出了关于小Teichmüller空间的一些等价刻画.     

Banach空间的K-极凸性、K-极光滑性

本文重新刻画了K-极凸空间与K-极光滑空间,并在此定义的基础上讨论了K-极凸空间与K-极光滑空间的对偶性;讨论了K-极凸空间与K-一致凸,K-强凸,K-DC等空间的关系;讨论了此种刻画与其它的定义之间的关系,并给出了一些等价定义,以及一些性质.     

完全分配格上的点式拟一致结构与p．q．度量

在完全分配格上建立了点式拟一致结构理论．讨论了诱导拓扑分子格中闭包，局部基，连续等性质．证明了每个拓扑分子格皆可点式拟一致化．另外借助纯距离函数与真正的远域映射族给出了［８］中ｐ．ｑ．度量的等价定义与刻画，得到了点式拟一致分子格的ｐ．ｑ．度量化定理．     

LOCAL HARDY SPACES ON HEISENBERG GROUP OVER LOCAL FIELDS

ＬＯＣＡＬＨＡＲＤＹＳＰＡＣＥＳＯＮＨＥＩＳＥＮＢＥＲＧＧＲＯＵＰＯＶＥＲＬＯＣＡＬＦＩＥＬＤＳ￥ＺｈｏｕＧｕａｎｇｃａｉ（周广才）（Ｄｅｐｔ．ｏｆＭａｔｈ．＆Ｍｅｃｈ．，ＳｏｕｔｈｅａｓｔＵｎｉｖｅｒｓｉｔｙ，Ｎａｎｊｉｎｇ２１００１８，Ｃｈｉｎａ...     

Lipschitz-Type Spaces and Hardy Spaces on Some Classes of Complex-Valued Functions

In this paper, we investigate the properties on some classes of complex-valued functions which satisfy certain elliptic equations. First, we discuss the Lipschitz-type spaces and Hardy spaces on these functions, and then we show that for a class of complex-valued functions, if it admits some bounded Dirichlet-type energy integral, then it has a harmonic majorant in the unit disk.     

Variable exponent Hardy spaces associated with discrete Laplacians on graphs

In this paper we develop the theory of variable exponent Hardy spaces associated with discrete Laplacians on infinite graphs. Our Hardy spaces are defined by square integrals, atomic and molecular decompositions. Also we study boundedness properties of Littlewood-Paley functions, Riesz transforms, and spectral multipliers for discrete Laplacians on variable exponent Hardy spaces.     

Hardy type spaces associated with compact unitary groups

We investigate Hilbertian Hardy type spaces of complex analytic functions of infinite many variables, associated with compact unitary groups and the corresponding invariant Haar’s measures. For such analytic functions we establish a Cauchy type integral formula and describe natural domains. Also we show some relations between constructed spaces of analytic functions and the symmetric Fock space.     

Reproducing kernel approximation in weighted Bergman spaces: Algorithm and applications

In this paper, we present algorithms of preorthogonal adaptive Fourier decomposition (POAFD) in weighted Bergman spaces. POAFD, as has been studied, gives rise to sparse approximations as linear combinations of the corresponding reproducing kernels. It is found that POAFD is unavailable in some weighted Hardy spaces that do not enjoy the boundary vanishing condition; as a result, the maximal selections of the parameters are not guaranteed. We overcome this difficulty with two strategies. One is to utilize the shift operator while the other is to perform weak POAFD. In the cases when the reproducing kernels are rational functions, POAFD provides rational approximations. This approximation method may be used to 1D signal processing. It is, in particular, effective to some Hardy H^p space functions for p not being equal to 2. Weighted Bergman spaces approximation may be used in system identification of discrete time‐varying systems. The promising effectiveness of the POAFD method in weighted Bergman spaces is confirmed by a set of experiments. A sequence of functions as models of the weighted Hardy spaces, being a wider class than the weighted Bergman spaces, are given, of which some are used to illustrate the algorithm and to evaluate its effectiveness over other Fourier type methods.     

Variable Hardy Spaces on the Heisenberg Group

We consider Hardy spaces with variable exponents defined by grand maximal function on the Heisenberg group. Then we introduce some equivalent characterizations of variable Hardy spaces. By using atomic decomposition and molecular decomposition we get the boundedness of singular integral operators on variable Hardy spaces. We investigate the Littlewood-Paley characterization by virtue of the boundedness of singular integral operators.     

调和函数的Lipschitz型空间和Landau-Bloch型定理

主要研究调和函数和Poisson方程的解的性质.讨论了调和函数的Lipschitz型空间,建立了调和函数的Schwarz-Pick型引理,并利用所得结果证明了与调和Hardy空间有关的一个Landau-Bloch型定理.最后,还利用正规族理论讨论了与Poisson方程的解有关的Landau-Bloch型定理的存在性.     

Representing measures and infinite-dimensional holomorphy

We consider some applications of the Bishop-De Leeuw Theorem about representing measures for some algebras of analytic functions on unit balls of Banach spaces. In particular, we investigate Hardy spaces H² associated with corresponding algebras. Some examples are considered.     

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.     

高阶交换子在Hardy空间上的连续性

本文研究了由齐性分数次积分和BMO函数生成的高阶交换子在某些Hardy空间、弱Hardy空间和Herz型Hardy空间上的连续性.