单位球上Dp到βμ的加权复合算子

讨论了单位球上D打ichlet型空间砩到μ-Bloch空间艮的加权复合算子的有界性和紧性问题,并给出了 Tψ,φ为有界算子和紧算子的充要条件．     

单位球上Dirichlet型空间D_q到β~p空间的加权Cesàro算子

本文研究了单位球B上Dirichlet空间Dq到βp空间的加权Cesàro算子的有界性和紧性问题.利用泛函分析多复变的方法,获得了单位球上Dirichlet型空间Dq到βp空间的加权Cesàro算子为有界算子和紧算子的充要条件.     

Composition operators on weighted Dirichlet spaces

We characterize bounded and compact composition operators on weighted Dirichlet spaces. The method involves integral averages of the determining function for the operator, and the connection between composition operators on Dirichlet spaces and Toeplitz operators on Bergman spaces. We also present several examples and counter-examples that point out the borderlines of the result and its connections to other themes.

     

Dirichlet型空间到-μBloch空间的加权Cesàro算子

主要讨论了Cn中单位球上Dirichlet型空间Dp到μ-Bloch空间βμ的加权Cesàro算子Tg的有界性和紧性问题,给出了Tg为Dp到βμ有界算子或紧算子的充要条件.     

Compact differences of composition operators

A characterization of compact difference is given for composition operators acting on the standard weighted Bergman spaces and necessary conditions are given on a larger scale of weighted Dirichlet spaces. Conditions are given under which a composition operator can be written as a finite sum of composition operators modulo the compacts. The additive structure of the space of composition operators modulo the compact operators is investigated further and a sufficient condition is given to insure that two composition operators lie in the same component.     

Nevanlinna and Carleson functions of analytic self‐maps on multiply‐connected domains

In the paper we prove that the Nevanlinna counting function and the Carleson function of analytic self‐maps of finitely connected domains with smooth boundary are equivalent. Using this result we obtain the characterization of compact composition operators on Hardy–Orlicz spaces.     

极大点空间的若干特征定理

本文利用极大点空间的等价刻划证明了极大点空间的某些子空间、不交和、 乘积空间、逆序列的逆极限、具有可数基的局部紧的Hausdorff空间是极大点空间,还 给出了具有可数基的局部紧的Hausdorff空间的Domain hull.     

Order Bounded Weighted Composition Operators Mapping into the Dirichlet Type Spaces

The authors characterize the order boundedness of weighted composition operators acting between Dirichlet type spaces.     

Dirichlet型空间上Hankel算子和乘法算子

本文讨论了Dirichlet型空间上的再生核,并对Dirichlet型空间上乘法算子,Hankel算子和小Hankel算子的基本性质进行了研究,同时也给出了这些算子的有界性,紧性和Schatten理想的初步刻画。     

μ-Bergman空间到Zygmund型空间的加权复合算子

本文研究了单位圆盘D上的μ-Bergman空间到Zygmund型空间的加权复合算子的有界性和紧性问题.利用泛函分析多复变的方法,获得了单位圆盘上μ-Bergman空间到Zygmund型空间的加权复合算子为有界算子和紧算子的充要条件.     

Polar actions on Hermitian and quaternion-Kähler symmetric spaces

We analyze polar actions on Hermitian and quaternion-Kähler symmetric spaces of compact type. For complex integrable polar actions on Hermitian symmetric spaces of compact type we prove a reduction theorem and several corollaries concerning the geometry of these actions. The results are independent of the classification of polar actions on Hermitian symmetric spaces. In the second part we prove that polar actions on Wolf spaces are quaternion-coisotropic and that isometric actions on these spaces admit an orbit of special type, analogous to the existence of a complex orbit for an isometric action on a compact homogeneous simply connected Kähler manifold.     

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。     

Besov空间到Zygmund空间上的加权复合算子

研究了单位圆盘上的Besov空间B_(p,q)到Zygmund空间Z的加权复合算子u C_φ(u∈Z),利用函数空间上的算子理论相关知识,得到了u C_φ:B_(p,q)→Z的有界性和紧性的充分必要条件.     

Haarlet analysis of Lipschitz regularity in metric measure spaces

In this note we shall give a characterization of Lipschitz spaces on spaces of homogeneous type via Haar coefficients.     

Compact composition operators on Besov spaces

We give a Carleson measure characterization of the compact composition operators on Besov spaces. We use this characterization to show that every compact composition operator on a Besov space is compact on the Bloch space. Finally we give conditions that guarantee that the converse holds.

     

支撑在(-1, 1)上的Carleson型测度与Hankel 矩阵

In this paper, we establish a connection between Carleson type measures supported on(-1, 1) and certain Hankel matrices. The connection is given by the study of Hankel matrices acting on Dirichlet type spaces.     

Composition operators between Bergman and Hardy spaces

We study composition operators between weighted Bergman spaces. Certain growth conditions for generalized Nevanlinna counting functions of the inducing map are shown to be necessary and sufficient for such operators to be bounded or compact. Particular choices for the weights yield results on composition operators between the classical unweighted Bergman and Hardy spaces.

     

Composition operators on Hilbert spaces of entire Dirichlet series

In this Note, we introduce Hilbert spaces of entire Dirichlet series (with real frequencies) and consider composition operators on these spaces. We establish necessary and sufficient conditions for such series to have Ritt order zero, as well as a finite logarithmic order. Criteria for action, boundedness, compactness and compact difference of such operators are obtained.     

Toeplitz Operators on Arveson and Dirichlet Spaces

We define Toeplitz operators on all Dirichlet spaces on the unit ball of and develop their basic properties. We characterize bounded, compact, and Schatten-class Toeplitz operators with positive symbols in terms of Carleson measures and Berezin transforms. Our results naturally extend those known for weighted Bergman spaces, a special case applies to the Arveson space, and we recover the classical Hardy-space Toeplitz operators in a limiting case; thus we unify the theory of Toeplitz operators on all these spaces. We apply our operators to a characterization of bounded, compact, and Schatten-class weighted composition operators on weighted Bergman spaces of the ball. We lastly investigate some connections between Toeplitz and shift operators. The research of the second author is partially supported by a Fulbright grant.     

Subspaces of Hilbert-generated Banach spaces and the quantification of super weak compactness

We introduce a measure of super weak noncompactness Γ defined for bounded subsets and bounded linear operators in Banach spaces that allows to state and prove a characterization of the Banach spaces which are subspaces of a Hilbert-generated space. The use of super weak compactness and Γ casts light on the structure of these Banach spaces and complements the work of Argyros, Fabian, Farmaki, Godefroy, Hájek, Montesinos, Troyanski and Zizler on this subject. A particular kind of relatively super weakly compact sets, namely uniformly weakly null sets, plays an important role and exhibits connections with Banach-Saks type properties.