Hankel operators on Fock spaces

Article English OPEN
Perala, A. ; Schuster, A. ; Virtanen, Jani A. (2014)
  • Publisher: Springer Basel
  • Related identifiers: doi: 10.1007/978-3-0348-0648-0_24
  • Subject:
    arxiv: Mathematics::Classical Analysis and ODEs | Mathematics::Functional Analysis

We study Hankel operators on the weighted Fock spaces\ud Fp. 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\ud Zhu's characterization of bounded and compact Hankel operators on Bergman spaces of the unit disk.
  • References (10)

    [3] Berndtsson, B.; Ortega Cerda, J., On interpolation and sampling in Hilbert spaces of analytic functions. J. Reine Angew. Math. 464 (1995), 109{128.

    [4] Bommier-Hato, H.; Youss , E., Hankel operators on weighted Fock spaces. Integral Equations Operator Theory 59 (2007), no. 1, 1{17.

    [5] Dostanic, M.; Zhu, K., Integral operators induced by the Fock kernel. Integral Equations and Operator Theory 60 (2008), 217{236.

    [6] Duren, P., Theory of Hp spaces. Academic Press, New York, 1970.

    [7] Isralowitz, J.; Zhu, K.; Toeplitz operators on the Fock space. Integral Equations and Operator Theory 66 (2010), no. 4, 593{611.

    [8] Janson, S.; Peetre, J.; Rochberg, R., Hankel forms and the Fock space. Rev. Mat. Iberoamericana 3 (1987), no. 1, 61{138.

    [9] Peller, V., Hankel operators and their applications. Springer-Verlag, New York, 2003.

    [10] Schuster, A.; Varolin, D., Toeplitz Operators and Carleson Measures on Generalized Bargmann-Fock Spaces. Integral Equations and Operator Theory, Volume 72, Number 3 (2012), 363{392.

    [11] Taskinen, J.; Virtanen, J. A., Weighted BM O and Toeplitz operators on the Bergman space A1. (to appear in Journal of Operator Theory).

    [12] Zhu, K., BMO and Hankel operators on Bergman spaces. Paci c J. Math. 155 (1992), 377{395.

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