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

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Abstract

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.

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References

  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)

    Article  MathSciNet  MATH  Google Scholar 

  2. Lin, P., Rochberg, R.: The essential norm of Hankel operator on the Bergman space. Integral Equ. Oper. Theory 17, 361–372 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  7. Zheng, D.: Toeplitz operators and Hankel operators. Integral Equ. Oper. Theory 12, 280–299 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  8. Zhu, K.: Duality and Hankel operators on the Bergman spaces of bounded symmetric domains. J. Funct. Anal. 81(2), 260–278 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  9. Zhu, K.: Hankel operators on the Bergman space of bounded symmetric domains. Trans. Am. Math. Soc. 324, 707–730 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  10. Zhu, K.: Operator Theory in Function Spaces, Mathematical Surveys and Monographs, vol. 138, 2nd edn. American Mathematical Society, Providence (2007)

    Book  Google Scholar 

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Acknowledgements

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

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Correspondence to Satoshi Yamaji.

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Communicated by H. Turgay Kaptanoglu.

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Yamaji, S. Essential Norm Estimates for Little Hankel Operators with Anti Holomorphic Symbols on the weighted Bergman Space of the Unit Disk. Complex Anal. Oper. Theory 13, 141–150 (2019). https://doi.org/10.1007/s11785-017-0752-7

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  • DOI: https://doi.org/10.1007/s11785-017-0752-7

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