Skip to main content

Quasihomogeneous Toeplitz operators on the harmonic Bergman space

Archiv der Mathematik volume 98, pages 49–60 (2012)Cite this article

Abstract

In this paper we study the product of Toeplitz operators on the harmonic Bergman space of the unit disk of the complex plane \({\mathbb{C}}\). Mainly, we discuss when the product of two quasihomogeneous Toeplitz operators is also a Toeplitz operator, and when such operators commute.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

39,95 €

Price includes VAT (Finland)

References

  1. Choe B. R., Lee Y. J.: Commuting Toeplitz operators on the harmonic Bergman space, Michigan Math. J 46, 163–174 (1999)

    MATH  MathSciNet  Google Scholar 

  2. Choe B.R., Lee Y.J.: Commutants of analytic Toeplitz operators on the harmonic Bergman space. Integral Equations Operator Theory 50, 559–564 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  3. C̆uc̆ković Z̆., Rao N.V.: Mellin transform, monomial Symbols, and commuting Toeplitz operators. J. Funct. Anal 154, 195–214 (1998)

    Article  MathSciNet  Google Scholar 

  4. Ding X.: A question of Toeplitz operators on the harmonic Bergman space. J. Math. Anal. Appl 344, 367–372 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  5. X. T. Dong and Z. H. Zhou, Products of Toeplitz operators on the harmonic Bergman space, Proc. Amer. Math. Soc. 138

  6. Louhichi I: Powers and roots of Toeplitz operators. Proc. Amer. Math. Soc 135, 1465–1475 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  7. Louhichi I., Strouse E., Zakariasy L.: Products of Toeplitz operators on the Bergman space. Integral Equations Operator Theory 54, 525–539 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  8. Louhichi I., Zakariasy L.: On Toeplitz operators with quasihomogeneous symbols. Arch. Math 85, 248–257 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  9. Remmert R.: Classical Topics in Complex Function Theory Graduate Texts in Mathematics. Springer, New York (1998)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    Issam Louhichi

  2. High Institute of Technology, 201, Antsiranana, Madagascar

    Lova Zakariasy

Authors
  1. Issam Louhichi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lova Zakariasy
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Issam Louhichi.

Additional information

The second author was partially supported by Agence Universitaire de la Francophonie.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Louhichi, I., Zakariasy, L. Quasihomogeneous Toeplitz operators on the harmonic Bergman space. Arch. Math. 98, 49–60 (2012). https://doi.org/10.1007/s00013-011-0346-y

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00013-011-0346-y

Mathematics Subject Classification (2010)

  • Primary 47B35
  • Secondary 47B38

Keywords

  • Toeplitz operator
  • Harmonic Bergman space
  • Quasihomogeneous symbol
  • Mellin transform