Bergman空间上的加权复合算子及应用(英文)

本文研究了单位圆盘上Bergman空间上的加权复合算子和复平面的单连通域(不是全平面)上Bergman空间上的复合算子的有界性和紧性.利用复分析方法,获得了有界性与紧性的一些充分条件和必要条件,推广了Hardy空间上的若干相关结果.     

WEIGHTED COMPOSITION OPERATORS ON BERGMAN SPACE AND APPLICATIONS

本文研究了单位圆盘上 Bergman空间上的加权复合算子和复平面的单连通域(不是全平面)上Bergrnan空间上的复合算子的有界性和紧性.利用复分析方法,获得了有界性与紧性的一些充分条件和必要条件,推广了Hardy空间上的若干相关结果.     

SEQUENCES OF POWERS OF TOEPLITZ OPERATORS ON THE BERGMAN SPACE

We consider Toeplitz operators Tu with symbol u on the Bergman space of the unit ball,and then study the convergences and summability for the sequences of power...     

高维加权Bergman空间上的Toeplitz算子

本文研究了高维加权Bergman空间Ap(Bn,dVpφ)(1＜p＜∞).上的Toeplitz算子.利用Toeplitz算子的Berezin变换,获得了Ap(Bn,dVp)(1＜p＜∞)上具有L∞(Bn)符号的Toeplitz算子的有限乘积的有限和是紧算子的一些等价刻画,推广了加权Bergman空间Ap(D,dmpφ)上的Toeplitz算子的有限乘积的有限和是紧的当且仅当它的Berezin变换在单位圆盘的边界消失为0的结论     

COLLECTIVELY COMPACT COMPOSITION OPERATOR SEQUENCES BETWEEN BERGMAN AND HARDY SPACES

This paper studies the collective compactness of composition operator se-quences between the Bergman and Hardy spaces. Some sufficient and necessary conditionsinvolving the generalized Nevanlinna counting functions for composition operator sequencesto be collectively compact between weighted Bergman spaces are given.     

加权Bergman空间上的约化子空间

主要证明在加权Bergman空间上符号为有限Blaskchke乘积的解析Toeplitz算子总是可约的,即至少有一个约化子空间.并且把该算子限制在该子空间上酉等价于加权Bergman位移.     

关于分数次Marcinkiewicz积分在Hardy空间上的有界性

本文研究了核函数粗糙的分数次Marcinkiewicz积分μΩ,α在Hardy空间上的有界性.利用Hardy空间的原子分解定理,获得了算子μΩ,α的H1,Ln-nα型和(Hp,Lq)型的有界性结果.     

TWO PROBLEMS ABOUT COMPOSITION OPERATORS ON HARDY SPACE

In this paper, two problems about composition operator on Hardy space are considered. Firstly, a new estimation of the norm of a class of composition operators is given. Secondly, the cyclic behavior of the adjoint operator of a composition operator is discussed.     

A CRITERION OF ESSENTIALLY COMMUTING TOEPLITZ OPERATORS ON BERGMAN SPACE

1.IntroductionLetmdenotethevolumemeastireontheunitballUnormalizedtohavetotalmass1ofthen-dimensionalcomplexspaceC".TheBergmanspaceBP(U)(15p相似文献   

Bergman空间上具有无界符号的迹类Toeplitz算子

本文研究了Bergman空间上具有无界符号的迹类Toeplitz算子的问题.利用构造的方法,获得了L2(Un,dA)中的函数φ,φ在Tn中每一点的任何邻域内都是无界的,并且使得Tφ是Bergman空间Lα2(Un,dA)上的迹类算子的结果.     

THE COMPACTNESS OF A KIND OF GENERALIZED HANKEL OPERATORS ON THE BERGMAN SPACE OF THE UNIT BALL

This paper gives the compactness criteria for a kind of generalized Hankel operators on Bergman spaces Lpa(B) defined by M.M.Peloso.     

THE ALL-ASSOCIATIVITY OF OCTONIONS AND ITS APPLICATIONS

Using an elementary method, we give a new proof of the all-associativity of octonions. As some applications, the known Taylor theorem is improved, and a new definition and new properties of octonionic determinant are also obtained.     

单位球上Bergman空间的Cesàro算子

对一切p∈(0,∞),Cesaro算子在加权的p次Bergman空间A p(Bn)上有界,但不是紧的,其中Bn是Cn上中的单位球,而是[0,1)上的正规权函数.与Cesaro算子相联系,以解析函数g为符号的积分箅子Rg定义为本文刻画了使算子Rg在A p(Bn)上是有界(或紧)的解析函数g的特征.同时,在多圆柱上也能得出类似的结果.     

第三类华罗庚域的Bergman核函数

本文主要是计算第三类华罗庚域的Bergman核函数的显式表达式.由于华罗庚域既不是齐性域又不是Reinhardt域,故以往求Bergman核函数的方法都行不通.本文用新的方法进行计算.关键之处有两点一是给出第三类华罗庚域的全纯自同构群,群中每一元素将形为(W,Z0)的内点映为点(W*,0);二是引进了semi-Reinhardt的概念并求出了其完备标准正交函数系.     

TOEPLITZ OPERATORS FROM HARDY SPACES TO WEIGHTED BERGMAN SPACES IN THE UNIT BALL OF Cn

We study Toeplitz operators from Hardy spaces to weighted Bergman spaces in the unit ball of Cⁿ.Toeplitz operators are closely related to many classical mappings,such as composition operators,the Volterra type integration operators and Carleson embeddings.We characterize the boundedness and compactness of Toeplitz operators from Hardy spaces H^p to weighted Bergman spaces A_α^q for the different values of p and q in the unit ball.     

第三类华罗庚域的Bergman核函数

本文主要是计算第三类华罗庚域的Bergman核函数的显式表达式.由于华罗庚域既不是齐性域又不是Reinhardt域,故以往求Bergman核函数的方法都行不通.本文用新的方法进行计算.关键之处有两点:一是给出第三类华罗庚域的全纯自同构群,群中每一元素将形为(W,Z0)的内点映为点(W*,0);二是引进了semi—Reinhardt的概念并求出了其完备标准正交函数系.     

THE BLOCH SPACE ON THE UNIT BALL OF A HILBERT SPACE:MAXIMALITY AND MULTIPLIERS

We prove that,as in the finite dimensional case,the space of Bloch functions on the unit ball of a Hilbert space contains,under very mild conditions,any semi-Ba...     

加权Bergman空间上的Carleson测度与复合算子

本文研究了复平面上单位圆盘D上具有指数型权的加权Bergman空间上的Carleson测度和复合算子。利用Carleson测度的概念分别给出了有界或紧的复合算子的充分必要条件。     

HANKEL OPERATORS ON HARDY SPACES AND SCHATTEN CLASSES

For a holomorphic function f on the unit ball B~N of C~N, it is proved that the reduced Hankel oporator R_f on Hardy space H~2(B~N) is of Schatten class S_p for p≥1 if and only if f is in a corresponding Sobolev space.     

加权Bergman空间上的Toeplitz算子和Hankel算子

西方给出了Ｃ＾ｎ中单位球上的带权的Ｂｅｒｇｍａｎ空间上具一般符号的Ｔｏｅｐｌｉｔｚ算子和Ｈａｎｋｅｌ算子为紧的充要条件。