Skip to main content
SpringerLink
Log in

M-harmonic Besovp-spaces and Hankel operators in the Bergman space on the ball in ℂn

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

Abstract

In this paper, we characterize the Hardy class ofM-harmonic functions on the unit ballB in ℂn in terms of the Berezin transform. We define and study the Besovp-spaces ofM-harmonic functions. For anM-harmonic symbolf, we give various criteria for the Hankel operatorsH f andH f to be bounded, compact or in the Schatten-von-Neumann classS p . These criteria establish a close relationship among Besovp-spaces, Berezin transform, the invariant Laplacian, and Hankel operators on the unit ballB.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. Arazy, S. Fisher andJ. Peetre,Möbius invariant function spaces, J. für die reine und angewandte Math., 363 (1985), pp. 110–145

    MathSciNet  MATH  Google Scholar 

  2. J. Arazy, S. Fisher andJ. Peetre,Hankel operators on weighted Bergman spaces, Amer. J. Math., 110 (1988), pp. 989–1054

    Article  MathSciNet  MATH  Google Scholar 

  3. S. Axler,The Bergman space, the Bloch space and commutators of multiplication operators, Duke Math. J., 53 (1986), pp. 315–332

    Article  MathSciNet  MATH  Google Scholar 

  4. C. A. Berger, L. A. Coburn andK. H. Zhu,Function theory in Cartan domains and the Berezin-Toeplitz symbol calculus, Amer. J. Math., 110 (1988), pp. 921–953

    Article  MathSciNet  MATH  Google Scholar 

  5. C. A. Berger, L. A. Coburn, andK. H. Zhu,BMO on the Bergman spaces of the classical domains, Bull. Amer. Math. Soc., 17, 1 (1987), pp. 133–136

    Article  MathSciNet  MATH  Google Scholar 

  6. K. T. Hahn,Holomorphic mappings of the hyperbolic space into the complex Euclidien space and the Bloch theorem, Can. J. Math., 27 (1975) pp. 446–458

    Article  MATH  Google Scholar 

  7. K. T. Hahn and E. H. Youssfi,Möbius invariant Besov p-spaces and Hankel Operators in the Bergman space on the ball in ℂ n, compl. Var. Th. Appl. (To appear)

  8. A. Kóranyi,Harmonic functions on hermitian hyperbolic space, Trans. Amer. Math. Soc.,135 (1969), pp. 507–516

    Article  MathSciNet  MATH  Google Scholar 

  9. W. Rudin,Function theory in the unit ball of ℂ n, Springer-Verlag, 1980

  10. R. M. Timoney,Bloch functions in several complex variables I, Bull. London Math. Soc., 12 (1980), pp. 241–267

    Article  MathSciNet  MATH  Google Scholar 

  11. D. Ullrich,Moebius invariant potential theory in the unit ball of ℂ n,Thesis, Univ. of Wisconson Madison 1981, University Microfilms International, Ann Arbor, Michigan, 1984

    Google Scholar 

  12. D. Zheng,Schatten class Hankel operators on the Bergman space, Integral Equations and Operator Theory, 13 (1990), pp. 442–459

    Article  MathSciNet  MATH  Google Scholar 

  13. K. H. Zhu,Hilbert-Schmidt Hankel operators on the Bergman space, Proc. Amer. Math. Soc., 109 (1990), pp. 721–730

    Article  MathSciNet  MATH  Google Scholar 

  14. K.H. Zhu,Schatten class Hankel operators on the Bergman space of the unit ball, preprint

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, The Pennsylvania State University, 16802, University Park, PA

    Kyong T. Hahn & E. H. Youssfi

Authors
  1. Kyong T. Hahn
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. H. Youssfi
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hahn, K.T., Youssfi, E.H. M-harmonic Besovp-spaces and Hankel operators in the Bergman space on the ball in ℂn . Manuscripta Math 71, 67–81 (1991). https://doi.org/10.1007/BF02568394

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02568394

Keywords

Search

Navigation