郭潔婷，譚海鷗

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郭潔婷，譚海鷗

（五邑大學(xué) 數(shù)學(xué)與計(jì)算科學(xué)學(xué)院，廣東 江門 529020）

令,分別是復(fù)平面上的單位開圓盤中的解析自映射和解析函數(shù). 加權(quán)復(fù)合算子定義為，，討論了該加權(quán)復(fù)合算子從Zygmund型空間到-Bloch空間的有界性.

加權(quán)復(fù)合算子；-Bloch空間；Zygmund型空間；有界性

1 預(yù)備知識(shí)

Bloch型空間到其他全純函數(shù)空間的復(fù)合算子與加權(quán)復(fù)合算子的研究成果詳見文獻(xiàn)[5-12]，關(guān)于Zygmund空間上的復(fù)合算子的有界性的一些特征見文獻(xiàn)[13-15]. 本文主要研究從Zygmund型空間到空間的加權(quán)復(fù)合算子的有界性，可看作是對文獻(xiàn)[16-17]中結(jié)果的推廣.

2 主要結(jié)果

首先給出有用的引理.

引理1[18]若，則

由式（6）和式（10），有：

由式（8）、式（11）和式（12），得證.

由式（8）、式（14）和式（15），得證.

由式（6）、式（8）、式（17）和式（18），得證.

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[6] OHNO S. Weighted composition operators betweenand the Bloch space [J]. Taiwanese J Math, 2001, 5(3): 555-563.

[7] ZHU Xiangling. Generalized weighted composition operators from Bloch-type spaces to weighted Bergman spaces [J]. Indian J Math, 2007, 49(2): 139-149.

[8] FU Xiaohong, ZHU Xiangling. Weighted composition operators on some weighted spaces in the unit ball [J]. Abstr Appl Anal, 2008(2): 1-8.

[9] LI Songxiao, STEVIC S. Weighted composition operators from Bergman-type spaces into Bloch spaces [J]. Proc Indian Acad Sci Math Sci, 2007, 117(3): 371-385.

[10] LI Songxiao, STEVIC S. Weighted composition operators fromto the Bloch space on the polydisk [J]. Abstr Appl Anal, 2007, 2007: 1-13.

[11] STEVIC S. Norm of weighted composition operators from Bloch space toon the unit ball [J]. Ars Combin, 2008, 88: 125-127.

[12] ZHU Xiangling. Weighted composition operators betweenand Bergman type spaces [J]. Commun Korean Math Soc, 2006, 21(4): 719-727.

[13] CHOE B, KOO H, SMITH W. Composition operators on small spaces [J]. Integr Equat Oper Th, 2006, 56(3): 357-380.

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[15] LI Songxiao, STEVIC S. Weighted composition operators from Zygmund spaces into Bloch spaces [J]. Applied Mathematics and Computation, 2008, 36(2): 825-831.

[16] 鄒堃，譚海鷗. 從Zygmund空間到Bloch-type空間的加權(quán)復(fù)合算子[J]. 青島理工大學(xué)學(xué)報(bào)，2010, 31(5): 105-108.

[17] SANATPOUR A H, HASSANLOU M. Essential norms of weighted composition operators between Zygmund-type spaces and Bloch-type spaces [J]. Turkish Journal of Mathematics, 2014, 38: 872-882.

[18] ESMARILI K, LINDSTORM M. Weighted composition operators between Zygmund type spaces and their essential norms [J]. Integr Equ Oper Teory, 2013, 75(4): 473-490.

[責(zé)任編輯：熊玉濤]

Weighted Composition Operators from Zygmund Type Spaces intoSpaces

GUOJie-ting, TANHai-ou

(School of Mathematics and Computational Science, Wuyi University, Jiangmen 529020, China)

Letbe an analytic self-map andbe a fixed analytic function in the open unit diskon the complex plane. The weighted composition operator is defined by,. This paper studies the boundedness of the weighted composition operators from Zygmund type spaces to-Bloch spaces.

weighted composition operators;-Bloch spaces; Zygmund type space; boundedness

1006-7302（2015）02-0006-06

O174.5

A

2014-12-03

郭潔婷（1989—），女，廣東鶴山人，在讀碩士生，研究方向?yàn)閺?fù)分析；譚海鷗，教授，碩士，碩士生導(dǎo)師，通信作者，研究方向?yàn)閺?fù)分析.