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BMO and Hankel Operators on Fock-Type Spaces

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Abstract

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 23:170–201, 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.

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Acknowledgments

Research of all authors supported by the China National Natural Science Foundation Grant No. 11271092. Research of Wang also supported by the Guangzhou Higher Education Science and Technology Project No. 2012A018

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Authors and Affiliations

  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

    Xiaofeng Wang & Guangfu Cao

  2. Department of Mathematics and Statistics, State University of New York, Albany, NY , 12222, USA

    Kehe Zhu

Authors
  1. Xiaofeng Wang
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  2. Guangfu Cao
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  3. Kehe Zhu
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Correspondence to Kehe Zhu.

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Communicated by Der-Chen Edward Chang.

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Wang, X., Cao, G. & Zhu, K. BMO and Hankel Operators on Fock-Type Spaces . J Geom Anal 25, 1650–1665 (2015). https://doi.org/10.1007/s12220-014-9488-z

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  • DOI: https://doi.org/10.1007/s12220-014-9488-z

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