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Hankel Operators on Fock Spaces

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Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 236))

Abstract

We study Hankel operators on the weighted Fock spaces Fp γ. The boundedness and compactness of these operators are characterized in terms of BMO and VMO, respectively. Along the way, we also study Berezin transform and harmonic conjugates on the plane. Our results are analogous to Zhu’s characterization of bounded and compact Hankel operators on Bergman spaces of the unit disk.

Mathematics Subject Classification (2010). Primary 47B35; Secondary 30H20, 30H35.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Helsinki, Helsinki, 00014, Finland

    A. Perälä

  2. Department of Mathematics, San Francisco State University, San Francisco, CA, 94132, USA

    A. Schuster

  3. Department of Mathematics and Actuarial Science, The American University in Cairo, AUC Avenue, 74, New Cairo, Egypt, 11835

    A. Schuster

  4. Department of Mathematics, University of Bristol, Bristol, England, BS8 1TW, UK

    J. A. Virtanen

Authors
  1. A. Perälä
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  2. A. Schuster
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  3. J. A. Virtanen
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Corresponding author

Correspondence to A. Perälä .

Editor information

Editors and Affiliations

  1. Departamento de Análisis Matemático, Universidad de Sevilla, Sevilla, Spain

    Manuel Cepedello Boiso

  2. Department of Mathematics, The Royal Institute of Technology, Stockholm, Sweden

    Håkan Hedenmalm

  3. Department of Mathematics & Computer Sci, Free University Amsterdam, Amsterdam, The Netherlands

    Marinus A. Kaashoek

  4. Departamento de Análisis Matemático, Universidad de Sevilla, Sevilla, Spain

    Alfonso Montes Rodríguez

  5. Department of Mathematics, Brown University, Providence, Rhode Island, USA

    Sergei Treil

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Perälä, A., Schuster, A., Virtanen, J.A. (2014). Hankel Operators on Fock Spaces. In: Cepedello Boiso, M., Hedenmalm, H., Kaashoek, M., Montes Rodríguez, A., Treil, S. (eds) Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation. Operator Theory: Advances and Applications, vol 236. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0648-0_24

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