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Journal d'Analyse Mathématique

, Volume 104, Issue 1, pp 13–23 | Cite as

Norm of Berezin transformon L p space

  • Milutin Dostanić
Article

Abstract

It is shown that the Berezin transform B on L p (D), where D is the unit disc, has norm \(\left\| B \right\|_p = \tfrac{{p + 1}}{{p^2 }}\tfrac{\pi }{{\sin (\pi /p)}}(1 < p \leqslant \infty )\). Furthermore, the norms of a family of operators (on L p (D)) whose kernels are moduli of Bergman type kernels are also calculated.

Keywords

Banach Space Unit Disc Toeplitz Operator Bergman Space Previous Inequality 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    F. A. Berezin, Covariant and contravariant symbols of operators, Math. USSR-Izv. 6 (1972), 1117–1151.CrossRefGoogle Scholar
  2. [2]
    K. Chandrasekharan, Arithmetical Functions, Springer-Verlag, New York-Berlin, 1970.zbMATHGoogle Scholar
  3. [3]
    M. R. Dostanić, Norm estimate of the Cauchy transform on L p (Ω), Integral Equations Operator Theory 52 (2005), 465–475.CrossRefMathSciNetzbMATHGoogle Scholar
  4. [4]
    G. H. Hardy, J. E. Littlewood, G. P’olya, Inequalities, 2nd ed., Cambridge University Press, 1952.Google Scholar
  5. [5]
    H. Hedenmalm, B. Korenblum, K. Zhu, Theory of Bergman Spaces, Springer-Verlag, New York, 2000.zbMATHGoogle Scholar
  6. [6]
    L. Hörmander, Notions of convexity, Birkhäuser Boston, Boston, MA, 1994.zbMATHGoogle Scholar
  7. [7]
    K. Zhu, Operator theory in Function spaces, Marcel Dekker, New York, 1990.zbMATHGoogle Scholar
  8. [8]
    K. Zhu, A sharp norm estimate of the Bergman projection on L p spaces, Bergman Spaces and Related Topics in Complex Analysis, Contemp. Math. 404 (2006), 195–205.Google Scholar

Copyright information

© The Hebrew University of Jerusalem 2008

Authors and Affiliations

  1. 1.Matematicki FakultetBeogradSerbia

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