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1.
Compactness of composition operators on BMOA 总被引:4,自引:0,他引:4
Wayne Smith 《Proceedings of the American Mathematical Society》1999,127(9):2715-2725
A function theoretic characterization is given of when a composition operator is compact on BMOA, the space of analytic functions on the unit disk having radial limits that are of bounded mean oscillation on the unit circle. When the symbol of the composition operator is univalent, compactness on BMOA is shown to be equivalent to compactness on the Bloch space, and a characterization in terms of the geometry of the image of the disk under the symbol of the operator results.
2.
本文研究了Bα(Bm)到BMOA(Bn)上的复合算子.利用Caxleson测度的等价条件,得到了Bα(Bm)到BMOA(Bn)上复合算子的有界和紧性的特征,推广了Bloch空间上复合算子的相应结果. 相似文献
3.
Compact Composition Operators on BMOA 总被引:8,自引:0,他引:8
P. S. Bourdon J. A. Cima A. L. Matheson 《Transactions of the American Mathematical Society》1999,351(6):2183-2196
We characterize the compact composition operators on BMOA, the space consisting of those holomorphic functions on the open unit disk that are Poisson integrals of functions on , that have bounded mean oscillation. We then use our characterization to show that compactness of a composition operator on BMOA implies its compactness on the Hardy spaces (a simple example shows the converse does not hold). We also explore how compactness of the composition operator relates to the shape of near , introducing the notion of mean order of contact. Finally, we discuss the relationships among compactness conditions for composition operators on BMOA, VMOA, and the big and little Bloch spaces.
4.
Eva A. Gallardo-Gutiérrez Jonathan R. Partington 《Journal of Functional Analysis》2010,258(11):3593-3603
Boundedness (resp. compactness) of weighted composition operators Wh,φ acting on the classical Hardy space H2 as Wh,φf=h(f○φ) are characterized in terms of a Nevanlinna counting function associated to the symbols h and φ whenever h∈BMOA (resp. h∈VMOA). Analogous results are given for Hp spaces and the scale of weighted Bergman spaces. In the latter case, BMOA is replaced by the Bloch space (resp. VMOA by the little Bloch space). 相似文献
5.
吕小芬 《数学物理学报(B辑英文版)》2012,32(2):559-567
In this article,we characterize the boundedness and compactness of extended Cesàro operators on the spaces BMOA by the Carleson measures in the unit ball.Mean-while,we study the pointwise multipliers o... 相似文献
6.
Manuel D. Contreras Santiago Díaz-Madrigal Dragan Vukotić 《Journal of Mathematical Analysis and Applications》2014
We obtain exhaustive results and treat in a unified way the question of boundedness, compactness, and weak compactness of composition operators from the Bloch space into any space from a large family of conformally invariant spaces that includes the classical spaces like BMOA , Qα, and analytic Besov spaces Bp. In particular, by combining techniques from both complex and functional analysis, we prove that in this setting weak compactness is equivalent to compactness. For the operators into the corresponding “small” spaces we also characterize the boundedness and show that it is equivalent to compactness. 相似文献
7.
Andrei N. Petrov 《Archiv der Mathematik》2013,100(6):551-560
We obtain sharp reverse estimates for the logarithmic Bloch spaces on the unit disk. As an application, we study composition operators with values in the space BMOA. 相似文献
8.
This paper deals with the boundedness and compactness of the weighted composition operators from the F(p, q, s) spaces, including Hardy space, Bergman space, Qp space, BMOA space, Besov space and α-Bloch space, to Bers-type spaces Hv^∞( or little Bers-type spaces Hv,o∞ ), where v is normal. 相似文献
9.
Jussi Laitila 《Integral Equations and Operator Theory》2007,58(4):487-502
Analytic composition operators
are studied on X-valued versions of BMOA, the space of analytic functions on the unit disk that have bounded mean oscillation on the unit
circle, where X is a complex Banach space. It is shown that if X is reflexive and C
φ is compact on BMOA, then C
φ is weakly compact on the X-valued space BMOA
C
(X) defined in terms of Carleson measures. A related function-theoretic characterization is given of the compact composition
operators on BMOA. 相似文献
10.
We study the weighted composition operators Wh,on Hardy space H2(B) whenever h ∈ BMOA(resp.h ∈ VMOA).Analogous results are given for Hp(B) spaces and the scale of weighted Bergman spaces.In the latter case,BMOA is replaced by the Bloch space(resp.VMOA by the little Bloch space). 相似文献
11.
12.
本文研究单位圆盘上的BMOA空间和α-Bloch型空间之间的加权Cesáro算子,给出了T_g是BMOA空间到B_α空间的有界算子或紧算子的充分必要条件。 相似文献
13.
设A是Rn上的各向异性伸缩, L是由各向异性Calderón-Zygmund算子生成的一般的多线性算子.本文得到L从加权Lebesgue空间Lwp(Rn)到无权的各向异性Hardy空间HAp (Rn)的有界性.另外,对各向异性Hardy空间H1(Rn)和加权各向异性BMO空间BMOAw(Rn)得到包含关系:BMOAw(Rn)■(H1A(Rn))*.作为应用,对加权各向异性BMO函数b和各向异性Calderón-Zygmund算子T生成的交换子[T, b],得到‖[T, b](f)‖Lwp(Rn)C‖b‖BMOwA(Rn)‖f‖Lpw(Rn).以上所有结果在经典的各向齐性情形下也是新的. 相似文献
14.
本文研究单位圆盘上的BMOA空间和$\a$-Bloch型空间之间的加权 Ces\'{a}ro 算子,给出了$\tg$是BMOA空间到$\ba$空间的有界算子或紧算子的充分必要条件. 相似文献
15.
Manuel D. Contreras Alfredo G. Hernández-Díaz 《Integral Equations and Operator Theory》2003,46(2):165-188
Let and be two analytic functions defined on such that. The operator given by is called a weighted composition
operator. In this paper we deal with the boundedness, compactness,
weak compactness, and complete continuity of weighted composition operators
from a Hardy space H
p
into another Hardy space H
q
.
We apply these results to study composition operators on Hardy spaces of a
half-plane.
Submitted: November 20, 2001. 相似文献
16.
In 2007, T. Hosokawa and S. Ohno gave the sufficient and necessary conditions
of the boundedness and compactness of differences of composition operators
on the Bloch space. On this base, this paper will generalize these conditions of the
boundedness and compactness of differences of composition operators on the Bloch
type space. 相似文献
17.
DENG Fangwen & OUYANG Caiheng Wuhan Institute of Physics Mathematics Chinese Academy of Sciences Wuhan China 《中国科学A辑(英文版)》2006,(11)
We give a definition of Bloch space on bounded symmetric domains in arbitrary complex Banach space and prove such function space is a Banach space. The properties such as boundedness, compactness and closed range of composition operators on such Bloch space are studied. 相似文献
18.
Using a geometric method, we characterize all entire functions that transform the Bloch space into a Bergman space by superposition
in terms of their order and type. We also prove that all superposition operators induced by such entire functions act boundedly.
Similar results hold for superpositions from BMOA into Bergman spaces and from the Bloch space into certain weighted Hardy
spaces. 相似文献
19.
We give a definition of Bloch space on bounded symmetric domains in arbitrary complex Banach space and prove such function
space is a Banach space. The properties such as boundedness, compactness and closed range of composition operators on such
Bloch space are studied.
Dedicated to Professor Sheng GONG on the occasion of his 75th birthday 相似文献
20.
Boo Rim Choe Hyungwoon Koo Wayne Smith 《Transactions of the American Mathematical Society》2003,355(7):2829-2855
We study the action of composition operators on Sobolev spaces of analytic functions having fractional derivatives in some weighted Bergman space or Hardy space on the unit disk. Criteria for when such operators are bounded or compact are given. In particular, we find the precise range of orders of fractional derivatives for which all composition operators are bounded on such spaces. Sharp results about boundedness and compactness of a composition operator are also given when the inducing map is polygonal.