Skip to main content
Log in

Difference of Weighted Composition Operators on Weighted-Type Spaces in the Unit Ball

  • Published:
Analysis Mathematica Aims and scope Submit manuscript

Abstract

In this paper, a new characterization is provided for the boundedness, compactness and essential norm of the difference of two weighted composition operators on weighted-type spaces in the unit ball of ℂn.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. E. Berkson, Composition operators isolated in the uniform operator topology, Proc. Amer. Math. Soc., 81 (1981), 230–232.

    Article  MathSciNet  Google Scholar 

  2. F. Colonna, New criteria for boundedness and compactness of weighted composition operators mapping into the Bloch space, Cent. Eur. J. Math., 11 (2013), 55–73.

    Article  MathSciNet  Google Scholar 

  3. C. Cowen and B. MacCluer, Composition Operators on Spaces of Analytic Functions, CRC Press (Boca Raton, FL, 1995).

    MATH  Google Scholar 

  4. J. Dai, Compact composition operators on the Bloch space of the unit ball, J. Math. Anal. Appl., 386 (2012), 294–299.

    Article  MathSciNet  Google Scholar 

  5. J. Dai and C. Ouyang, Differences of weighted composition operators on \(H_\alpha^\infty \left({{B_N}} \right)\), J. Inequal. Appl., 2009 (2009), Article ID 127431, 19 pp.

  6. Q. Hu, S. Li and Y. Shi, A new characterization of differences of weighted composition operators on weighted-type spaces, Comput. Methods Funct. Theory, 17 (2017), 303–318.

    Article  MathSciNet  Google Scholar 

  7. Q. Hu, S. Li and H. Wulan, New essential norm estimates of weighted composition operators from H into the Bloch space, Complex Var. Elliptic Equ., 62 (2017), 600–615.

    Article  MathSciNet  Google Scholar 

  8. S. Li, Differences of generalized composition operators on the Bloch space, J. Math. Anal. Appl., 394 (2012), 706–711.

    Article  MathSciNet  Google Scholar 

  9. M. Lindstrom and E. Wolf, Essential norm of the difference of weighted composition operators, Monatsh. Math., 153 (2008), 133–143.

    Article  MathSciNet  Google Scholar 

  10. X. Liu and S. Li, Norm and essential norm of a weighted composition operator on the Bloch space, Integr. Equ. Oper. Theory, 87 (2017), 309–325.

    Article  MathSciNet  Google Scholar 

  11. J. Moorhouse, Compact differences of composition operators, J. Funct. Anal., 219 (2005), 70–92.

    Article  MathSciNet  Google Scholar 

  12. P. Nieminen, Compact differences of composition operators on Bloch and Lipschitz spaces, Comput. Method Funct. Theory, 7 (2007), 325–344.

    Article  MathSciNet  Google Scholar 

  13. E. Saukko, Difference of composition operators between standard weighted Bergman spaces, J. Math. Anal. Appl., 381 (2011), 789–798.

    Article  MathSciNet  Google Scholar 

  14. E. Saukko, An application of atomic decomposition in Bergman spaces to the study of differences of composition operators, J. Funct. Anal., 262 (2012), 3872–3890.

    Article  MathSciNet  Google Scholar 

  15. J. Shapiro and C. Sundberg, Isolation amongst the composition operators, Pacific J. Math., 145 (1990), 117–152.

    Article  MathSciNet  Google Scholar 

  16. Y. Shi and S. Li, Essential norm of the differences of composition operators on the Bloch space, Math. Ineqal. Appl., 20 (2017), 543–555.

    MathSciNet  MATH  Google Scholar 

  17. Y. Shi and S. Li, Differences of composition operators on Bloch type spaces, Complex Anal. Oper. Theory, 11 (2017), 227–242.

    Article  MathSciNet  Google Scholar 

  18. H. Wulan, D. Zheng and K. Zhu, Compact composition operators on BMOA and the Bloch space, Proc. Amer. Math. Soc., 137 (2009), 3861–3868.

    Article  MathSciNet  Google Scholar 

  19. R. Zhao, Essential norms of composition operators between Bloch type spaces, Proc. Amer. Math. Soc., 138 (2010), 2537–2546.

    Article  MathSciNet  Google Scholar 

  20. K. Zhu, Spaces of Holomorphic Functions in the Unit Ball, Springer-Verlag (2004).

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to S. Li.

Additional information

This project was funded by the Science and Technology Development Fund, Macau SAR (file no. 186/2017/A3) and NNSF of China (No. 11720101003).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hu, B., Li, S. Difference of Weighted Composition Operators on Weighted-Type Spaces in the Unit Ball. Anal Math 46, 517–533 (2020). https://doi.org/10.1007/s10476-020-0036-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10476-020-0036-8

Key words and phrases

Mathematics Subject Classification

Navigation