BMO and Hankel Operators on Fock-Type Spaces

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• 作者：Xiaofeng Wang ; Guangfu Cao ; Kehe Zhu
• 关键词：Generalized Fock space ; Hankel operator ; Toeplitz operator ; BMO ; Berezin transform ; Primary 47B35 ; 30H20 ; Secondary 32A36 ; 32A37
• 刊名：Journal of Geometric Analysis
• 出版年：2015
• 出版时间：July 2015
• 年：2015
• 卷：25
• 期：3
• 页码：1650-1665
• 全文大小：432 KB
• 参考文献：1.Bekolle, D., Berger, C., Coburn, L., Zhu, K.: BMO in the Bergman metric on bounded symmetric domains. J. Funct. Anal. 93, 310-50 (1990)MATH MathSciNet View Article
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  13.Seip, K., Youssfi, E.H.: Hankel operators on Fock spaces and related Bergman kernel estimates. J. Geom. Anal. 23, 170-01 (2013)MATH MathSciNet View Article
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• 作者单位：Xiaofeng Wang (1)
  Guangfu Cao (1)
  Kehe Zhu (2)
  
  1. School of Mathematics and Information Science and Key Laboratory of Mathematics and Interdisciplinary Sciences of the Guangdong Higher Education Institute, Guangzhou University, Guangzhou?, 510006, China
  2. Department of Mathematics and Statistics, State University of New York, Albany, NY?, 12222, USA
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Differential Geometry
  Convex and Discrete Geometry
  Fourier Analysis
  Abstract Harmonic Analysis
  Dynamical Systems and Ergodic Theory
  Global Analysis and Analysis on Manifolds
  
• 出版者：Springer New York
• ISSN：1559-002X

文摘

In this paper we consider Hankel operators on a family of Fock-type spaces and characterize their boundedness and compactness in terms of a certain notion of bounded and vanishing mean oscillation. This extends the main results of Seip and Youssfi (J Geom Anal 23:170-01, 2013) to symbol functions that are not necessarily anti-holomorphic. We also give geometric descriptions for the spaces BMO and VMO which were defined in terms of the Berezin transform.