Complex Analysis and Operator Theory

, Volume 13, Issue 1, pp 141–150 | Cite as

Essential Norm Estimates for Little Hankel Operators with Anti Holomorphic Symbols on the weighted Bergman Space of the Unit Disk

  • Satoshi YamajiEmail author


We give estimates for the essential norm of little Hankel operators with anti holomorphic symbols on weighted Bergman spaces of the unit disk in terms of the Bloch semi norm of its symbol function.


Little Hankel operator Essential norm Bergman space Bergman kernel 

Mathematics Subject Classification




The author would like to thank the referees for giving useful comments.


  1. 1.
    Čučković, Ž., Zhao, R.: Essential norm of weighted composition operators between Bergman spaces on strongly pseudoconvex domains. Math. Proc. Camb. Philos. Soc. 142, 525–533 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Lin, P., Rochberg, R.: The essential norm of Hankel operator on the Bergman space. Integral Equ. Oper. Theory 17, 361–372 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Luo, L.: The essential norm of Toeplitz operators between Bergman spaces of the unit ball in \(\mathbb{C}^{n}\). Complex Anal. Oper. Theory 9(2), 265–273 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Luo, L., Xuemei, Y.: The essential norm of the generalized Hankel operators on the Bergman space of the unit ball in \(\mathbb{C}^{n}\). Abstr. Appl. Anal., Art. 2010, 343578 (2010)Google Scholar
  5. 5.
    Yamaji, S.: Positive Toeplitz operators on weighted Bergman spaces of a minimal bounded homogeneous domain. J. Math. Soc. Jpn. 65(4), 1101–1115 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Yamaji, S.: Essential norm estimates for little Hankel operators on weighted Bergman spaces of the unit ball. Complex Anal. Oper. Theory 8, 863–873 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Zheng, D.: Toeplitz operators and Hankel operators. Integral Equ. Oper. Theory 12, 280–299 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Zhu, K.: Duality and Hankel operators on the Bergman spaces of bounded symmetric domains. J. Funct. Anal. 81(2), 260–278 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Zhu, K.: Hankel operators on the Bergman space of bounded symmetric domains. Trans. Am. Math. Soc. 324, 707–730 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Zhu, K.: Operator Theory in Function Spaces, Mathematical Surveys and Monographs, vol. 138, 2nd edn. American Mathematical Society, Providence (2007)CrossRefGoogle Scholar

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© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Kobe City College of TechnologyKobeJapan

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