Skip to main content
SpringerLink
Log in

Toeplitz operators on weighted Besov spaces of holomorphic functions on the polydisk

  • Functional Analysis
  • Published:
Journal of Contemporary Mathematical Analysis Aims and scope Submit manuscript

Abstract

We characterize symbols h for which the corresponding Toeplitz operators are bounded on weighted Besov spaces B p (ω) of holomorphic functions on the polydisk for some 1 ≤ p < ∞.

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, J. Peetre, “Mobius invariant function spaces”, J. Reine Angew.Math., 363, 110–145, 1985.

    MathSciNet  MATH  Google Scholar 

  2. O. Blasco, “Multipliers on weighted Besov spaces of analytic functions”, Contemporary Mathematics, 144, 23–33, 1993.

    Article  MathSciNet  Google Scholar 

  3. M. M. Djrbashian, “On the representation problemof analytic functions”, Soobsh. Inst.Matem.Mekh. Akad. Nauk Arm. SSR, 2, 3–40, 1948.

    Google Scholar 

  4. V. S. Guliyev, W. Zhijian, “Weighted holomorphic Besov spaces and their boundary values”, Anal. Theory App., 21 (2), 143–156, 2005.

    Article  MATH  Google Scholar 

  5. A. V. Harutyunyan, “Bloch spaces of holomorphic functions in the polydisk”, J. Funct. Spaces Appl., 5 (3), 213–230, 2007.

    Article  MathSciNet  MATH  Google Scholar 

  6. A. V. Harutyunyan, G. V. Harutyunyan, “Holomorphic Besov spaces in the polydisc and bounded Toeplitz operators”, Analysis, 30 (4), 365–381, 2010.

    MathSciNet  MATH  Google Scholar 

  7. A. V. Harutyunyan, W. Lusky, “Duals of holomorphic Besov spaces on the polydisk and diagonal mappings”, Journal of ContemporaryMathematical Analysis (Armenian Academy of Sciences) 45 (3), 128–135, 2010.

    Google Scholar 

  8. A. V. Harutyunyan, W. Lusky, “Weighted holomorphic Besov spaces on the polydisks”, J. Funct. Spaces and Appl., 9, 1–16, 2011.

    Article  MathSciNet  MATH  Google Scholar 

  9. M. Jevtic, “Holomorphic Besov spaces on bounded symetric domains”, Filomat, 12 (1), 1988.

    Google Scholar 

  10. W. Rudin, Function Theory in Polydiscs (New York, 1969).

    MATH  Google Scholar 

  11. F. Shamoyan, “Diagonal mappincs and questions of presentation in anisotropic spaces in Polydisk”, Sib. mat. Journ., 3 (2), 197–215, 1990.

    MathSciNet  Google Scholar 

  12. E. Seneta, Functions of Regular Variation (Nauka, Moscow, 1985).

    Google Scholar 

  13. K. Zhu, Operator Theory in Function Spaces, (Marcel Dekker, New York, 1990).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Yerevan State University, Yerevan, Armenia

    A. Harutyunyan

  2. University of Paderborn, Paderborn, Germany

    W. Lusky

Authors
  1. A. Harutyunyan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. W. Lusky
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to A. Harutyunyan or W. Lusky.

Additional information

Original Russian Text © A. Harutyunyan, W. Lusky, 2015, published in Izvestiya NAN Armenii. Matematika, 2015, No. 4, pp. 36-50.

Supported by Deutsche Forschungsgemeinschaft LU 219/9-1

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Harutyunyan, A., Lusky, W. Toeplitz operators on weighted Besov spaces of holomorphic functions on the polydisk. J. Contemp. Mathemat. Anal. 50, 176–186 (2015). https://doi.org/10.3103/S1068362315040032

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1068362315040032

Keywords

MSC2010 numbers

Search

Navigation