Skip to main content
SpringerLink
Log in

Essential Norm of Weighted Composition Operators from the Lipschtiz Space to the Zygmund Space

  • Published:
Bulletin of the Malaysian Mathematical Sciences Society Aims and scope Submit manuscript

Abstract

In this paper, we give some estimates for the essential norm of weighted composition operators from the Lipschitz space to the Zygmund space.

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

Access this article

Log in via an institution

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Similar content being viewed by others

References

  1. Choe, B., Koo, H., Smith, W.: Composition operators on small spaces. Integral Equ. Oper. Theory 56, 357–380 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  2. Clahane, D., Stević, S.: Norm equivalence and composition operators between Bloch/Lipschitz spaces of the ball. J. Inequal. Appl. 2006, 11 (2006)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  4. Colonna, F., Li, S.: Weighted composition operators from \(H^\infty \) into the Zygmund spaces. Complex Anal. Oper. Theory 7, 1495–1512 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  5. Colonna, F., Li, S.: Weighted composition operators from the Lipschtiz space into the Zygmund space. Math. Inequal Appl. 17, 963–975 (2014)

    MathSciNet  MATH  Google Scholar 

  6. Cowen, C., MacCluer, B.D.: Composition Operators on Spaces of Analytic Functions Studies in Advanced Mathematics. CRC Press, Boca Raton (1995)

    MATH  Google Scholar 

  7. Duren, P.: Theory of \(H^p\) Spaces. Academic Press, New York (1970)

    MATH  Google Scholar 

  8. Esmaeili, K., Lindström, M.: Weighted composition operators between Zygmund type spaces and their essential norms. Integral Equ. Oper. Theory 75, 473–490 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  9. Hu, Q., Ye, S.: Weighted composition operators on the Zygmund spaces. Abstr. Appl. Anal. 2012, (2012)

  10. Hyvärinen, O., Lindström, M.: Estimates of essential norm of weighted composition operators between Bloch-type spaces. J. Math. Anal. Appl. 393, 38–44 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  11. Li, H., Fu, X.: A new characterization of generalized weighted composition operators from the Bloch space into the Zygmund space. J. Funct. Spaces Appl. 2013, 12 (2013)

    MathSciNet  MATH  Google Scholar 

  12. Li, S., Stević, S.: Volterra type operators on Zygmund spaces. J. Inequal. Appl. 2007, 10 (2007)

  13. Li, S., Stević, S.: Generalized composition operators on Zygmund spaces and Bloch type spaces. J. Math. Anal. Appl. 338, 1282–1295 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  14. Li, S., Stević, S.: Weighted composition operators from Zygmund spaces into Bloch spaces. Appl. Math. Comput. 206, 825–831 (2008)

    MathSciNet  MATH  Google Scholar 

  15. Li, S., Stević, S.: Products of Volterra type operator and composition operator from \(H^\infty \) and Bloch spaces to the Zygmund space. J. Math. Anal. Appl. 345, 40–52 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  16. Li, S., Stević, S.: Integral-type operators from Bloch-type spaces to Zygmund-type spaces. Appl. Math. Comput. 215, 464–473 (2009)

    MathSciNet  MATH  Google Scholar 

  17. Li, S., Stević, S.: Products of composition and differentiation operators from Zygmund spaces to Bloch spaces and Bers spaces. Appl. Math. Comput. 217, 3144–3154 (2010)

    MathSciNet  MATH  Google Scholar 

  18. Maccluer, B., Zhao, R.: Essential norm of weighted composition operators between Bloch-type spaces. Rocky Mountain J. Math. 33, 1437–1458 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  19. Madigan, K., Matheson, A.: Compact composition operators on the Bloch space. Trans. Am. Math. Soc. 347, 2679–2687 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  20. Manhas, J., Zhao, R.: New estimates of essential norms of weighted composition operators between Bloch type spaces. J. Math. Anal. Appl. 389, 32–47 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  21. Montes-Rodriguez, A.: The essential norm of composition operators on the Bloch space. Pac. J. Math. 188, 339–351 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  22. Ohno, S., Stroethoff, K., Zhao, R.: Weighted composition operators between Bloch-type spaces. Rocky Mountain J. Math. 33, 191–215 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  23. Stević, S.: Norms of some operators from Bergman spaces to weighted and Bloch-type space. Util. Math. 76, 59–64 (2008)

    MathSciNet  MATH  Google Scholar 

  24. Stević, S.: On Lipschitz and \(\alpha \)-Bloch spaces on the unit polydisc. Stud. Sci. Math. Hungar. 45, 361–378 (2008)

    MathSciNet  MATH  Google Scholar 

  25. Stević, S.: On an integral operator from the Zygmund space to the Bloch-type space on the unit ball. Glasg. J. Math. 51, 275–287 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  26. Stević, S.: Composition operators from the Hardy space to the Zygmund-type space on the upper half-plane. Abstr. Appl. Anal. 2009, 8 (2009)

  27. Stević, S.: On an integral-type operator from Zygmund-type spaces to mixed-norm spaces on the unit ball. Abstr. Appl. Anal. 2010, 7 (2010)

  28. Stević, S.: Weighted differentiation composition operators from mixed-norm spaces to the \(n-\)th weighted-type space on the unit disk. Abstr. Appl. Anal. 2010, 15 (2010)

  29. Stević, S.: Weighted differentiation composition operators from \(H^\infty \) and Bloch spaces to \(n\)th weighted-type spaces on the unit disk. Appl. Math. Comput. 216, 3634–3641 (2010)

    MathSciNet  MATH  Google Scholar 

  30. Tjani, M.: Compact composition operators on some Möbius invariant Banach spaces, Ph.D. dissertation, Michigan State University, Michigan (1996)

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Shantou University, Shantou, 515063, Guangdong, People’s Republic of China

    Qinghua Hu

  2. Department of Mathematics, Jiaying University, Meizhou, 514015, Guangdong, People’s Republic of China

    Xiangling Zhu

Authors
  1. Qinghua Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiangling Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiangling Zhu.

Additional information

Communicated by V. Ravichandran.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hu, Q., Zhu, X. Essential Norm of Weighted Composition Operators from the Lipschtiz Space to the Zygmund Space. Bull. Malays. Math. Sci. Soc. 41, 1293–1307 (2018). https://doi.org/10.1007/s40840-016-0391-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40840-016-0391-6

Keywords

Mathematics Subject Classification

Search

Navigation