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从Zygmund空间到Bloch-type空间的加权复合算子 被引量：2

Weighted Composition Operators from Zygmund Spaces into Bloch-type Spaces
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摘要 令φ,u分别是复平面C上的单位开圆盘D中的解析自映射和解析函数.加权复合算子定义为(uCφ)(f)(z)=u(z)f(φ(z)),z∈D,f∈H(D).主要讨论了从Zygmund空间到Bloch-type空间的加权复合算子的有界性和紧性. Let φ be an analytic self-map and u be a fixed analytic function in the open unit disk D on the complex plane C.The weighted composition operator is defined by（uC_φ）（f）（z）=u（z）f（φ（z））,z∈D,f∈H（D）.This paper studies the boundedness and compactness of the weighted composition operators from Zygmund spaces to Bloch-type spaces.
作者 邹堃 谭海鸥
机构地区 五邑大学数学与计算科学学院
出处 《青岛理工大学学报》 CAS 2010年第5期105-108,共4页 Journal of Qingdao University of Technology
关键词 加权复合算子 ZYGMUND空间 Bloch-type空间 有界性 紧性 weighted composition operator Zygmund space Bloch-type space boundedness compactness
分类号 O174.5 [理学—基础数学] O177.2 [理学—基础数学]
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参考文献18

  • 1Zhu K. Operator Theory in Functions Spaces[M]. New York: Springer, 1990.
  • 2Cowen C C, Maccluer B D. Composition Operator on Spaces of Analytic Functions[M]. Boca Raton:CRC Press, 1995.
  • 3Duren P L. Theory of H^p Spaces[M]. New York: Academic Press, 1970.
  • 4Li S, Stevie S. Volterra Type Operators on Zygmund Space[J]. J Inequal Appl, 2007, 2007:1-10.
  • 5Ohno S, Stroethoff K, Zhao R. Weighted Composition Operators Between Bloch-type Spaces[J]. Rocky Mountain J Math, 2003, 33 (1): 191-215.
  • 6Ohno S. Weighted Composition Operators Between H^∞ and the Bloch Space[J]. Taiwan Residents J Math, 2001, 5 (3): 555-563.
  • 7Stevic S. Composition Operators Between H^∞: and the α-Bloeh Spaces on the Polydisk[J]. Z Anal Anwend, 2006, 25 (4) : 457-466.
  • 8Stevic S. Norm of Weighted Composition Operators from Bloch Space to Hμ^∞ on the Unit Ball[J]. Ars Combin, 2008, 88: 125-127.
  • 9Zhu X. Weighted Composition Operators Between H∞ and Bergman Type Spaces[J]. Commun Korean Math Soc, 2006, 21 (4): 719- 727.
  • 10Zhu X. Generalized Weighted Composition Operators from Bloch-type Spaces to Weighted Bergman Spaces[J]. Indian J Math, 2007, 49 (2): 139-149.

同被引文献22

  • 1ZHU Kehe. Operator Theory in Functions Spaces [M]. New York: Springer, 1990.
  • 2COWEN C C, MACCLUER B D. Composition Operator on Spaces of Analytic Functions [M]. Boca Rat on: CRC Press, 1995.
  • 3DUREN P L. Theory of Hp Spaces [M]. New York: Academic Press, 1970.
  • 4LI Songxiao, STEVIC S. Volterra type operators on Zygmund space [J]. J Inequal Appl, 2007(1): 1-10.
  • 5OHNO S, STROETHOFF K, ZHAO Ruhan. Weighted composition operators between Bloch-type spaces [J]. Rocky Mountain J Math, 2003, 33(1): 191-215.
  • 6OHNO S. Weighted composition operators between H" and the Bloch space [J]. Taiwan Residents J Math, 2001, 5(3)555-563.
  • 7ZHU Xiangling. Generalized weighted composition operators from Bloch-type spaces to weighted Bergman spaces [J]. Indian J Math, 2007, 49(2): 139-149.
  • 8FU Xiaohong, ZHU Xiangling. Weighted composition operators on some weighted spaces in the unit ball [J]. Abstr Appl Anal, 2008(2): 1-8.
  • 9LI 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.
  • 10LI Songxiao, STEVIC S. Weighted composition operators from H" to the Bloch space on the polydisk [J]. Abstr Appl Anal, 2007; 2007: 1-13.

引证文献2

青岛理工大学学报
2010年 第5期

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