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Schatten(-Herz) class extended Cesàro operators on Bergman spaces in the unit ball of $ {\mathbf{C}}^n$


Authors: Zhangjian Hu and Xiaomin Tang
Journal: Proc. Amer. Math. Soc. 138 (2010), 2803-2814
MSC (2010): Primary 47B38; Secondary 47B35, 32A36
DOI: https://doi.org/10.1090/S0002-9939-10-10365-7
Published electronically: March 26, 2010
MathSciNet review: 2644894
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Abstract: For a large class of weights $ \varphi$, we characterize the holomorphic symbols $ g$, for which the extended Cesàro operators $ T_g$ acting on the weighted Bergman space $ A^2_\varphi({\mathbf B})$ are in the Schatten (or Schatten-Herz) class in the unit ball of $ \mathbf{C}^n$.


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Additional Information

Zhangjian Hu
Affiliation: Department of Mathematics, Huzhou Teachers College, Huzhou, Zhejiang 313000, People’s Republic of China
Email: huzj@hutc.zj.cn

Xiaomin Tang
Affiliation: Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China – and – Department of Mathematics, Huzhou Teachers College, Huzhou, Zhejiang 313000, People’s Republic of China
Email: txm@hutc.zj.cn

DOI: https://doi.org/10.1090/S0002-9939-10-10365-7
Keywords: Extended Ces\`{a}ro operator, Schatten class, Schatten-Herz class, Bergman space.
Received by editor(s): April 2, 2009
Received by editor(s) in revised form: November 5, 2009
Published electronically: March 26, 2010
Additional Notes: This project is supported by the National Natural Science Foundation of China (Nos. 10771064, 10971063), the Natural Science Foundation of Zhejiang Province (Nos. Y7080197, D7080080) and the Innovation Team Foundation of the Department of Education of the Zhejiang Province (No. T200924)
Communicated by: Marius Junge
Article copyright: © Copyright 2010 American Mathematical Society

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