Skip to main content
Log in

Product-Type Operators from the Bloch Space into Zygmund-Type Spaces

  • Original Paper
  • Published:
Bulletin of the Iranian Mathematical Society Aims and scope Submit manuscript

Abstract

Some characterizations for the boundedness, compactness and essential norm of a class of product-type operators \(T^n_{u,v,\varphi }\) from the Bloch space and little Bloch space into Zygmund-type spaces are given in this paper.

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.

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.

References

  1. Abbasi, E., Vaezi, H.: Generalized weighted composition operators from the Bloch-type spaces to the weighted Zygmund spaces. Filomat 33, 981–992 (2019)

    Article  MathSciNet  Google Scholar 

  2. Cowen, C.C., MacCluer, B.D.: Composition Operators on Spaces of Analytic Functions. CRC Press, Boca Raton (1995)

    MATH  Google Scholar 

  3. Du, J., Li, S., Zhang, Y.: Essential norm of generalized composition operators on Zygmund type spaces and Bloch type spaces. Ann. Polon. Math. 119, 107–119 (2017)

    Article  MathSciNet  Google Scholar 

  4. Du, J., Li, S., Zhang, Y.: Essential norm of weighted composition operators on Zygmund-type spaces with normal weight. Math. Inequal. Appl. 21, 701–714 (2018)

    MathSciNet  MATH  Google Scholar 

  5. Hu, Q., Li, S., Zhang, Y.: Essential norm of weighted composition operators from analytic Besov spaces into Zygmund type spaces. J. Contemp. Math. Anal. 54(3), 129–142 (2019)

    Article  MathSciNet  Google Scholar 

  6. Jiang, Z.: Product-type operators from Zygmund spaces to Bloch–Orlicz spaces. Complex Var. Elliptic Equ. 62, 1645–1664 (2017)

    Article  MathSciNet  Google Scholar 

  7. 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) (article ID 925901)

  8. Li, S., Stević, S.: Volterra type operators on Zygmund spaces. J. Inequal. Appl. (2007) (article ID 32124)

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

    MathSciNet  MATH  Google Scholar 

  10. Li, S., Stević, S.: Generalized weighted composition operators from \(\alpha \)-Bloch spaces into weighted-type spaces. J. Inequal. Appl. 2015, 265 (2015)

    Article  MathSciNet  Google Scholar 

  11. Liu, Y., Yu, Y.: Products of composition, multiplication and radial derivative operators from logarithmic Bloch spaces to weighted-type spaces on the unit ball. J. Math. Anal. Appl. 423, 76–93 (2015)

    Article  MathSciNet  Google Scholar 

  12. Liu, Y., Yu, Y.: The product-type operators from logarithmic Bloch spaces to Zygmund-type spaces. Filomat 33, 3639–3653 (2019)

    Article  MathSciNet  Google Scholar 

  13. MacCluer, B.D., Zhao, R.: Essential norms of weighted composition operators between Bloch-type spaces. Rocky Mt. J. Math. 33, 1437–1458 (2003)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  15. Stević, S.: Weighted differentiation composition operators from mixed-norm spaces to weighted-type spaces. Appl. Math. Comput. 211, 222–233 (2009)

    MathSciNet  MATH  Google Scholar 

  16. Stević, S.: Weighted differentiation composition operators from the mixed-norm space to the nth weighted-type space on the unit disk. Abstr. Appl. Anal. (2010) (article ID 246287)

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

    MathSciNet  MATH  Google Scholar 

  18. Stević, S., Sharma, A.: On a product-type operator between Hardy and \(\alpha \)-Bloch spaces of the upper half-plane. J. Inequal. Appl. 2018, 273 (2018)

    Article  MathSciNet  Google Scholar 

  19. Stević, S., Sharma, A., Bhat, A.: Products of multiplication composition and differentiation operators on weighted Bergman spaces. Appl. Math. Comput. 217, 8115–8125 (2011)

    MathSciNet  MATH  Google Scholar 

  20. Stević, S., Sharma, A., Bhat, A.: Essential norm of products of multiplications composition and differentiation operators on weighted Bergman spaces. Appl. Math. Comput. 218, 2379–2386 (2011)

    MathSciNet  MATH  Google Scholar 

  21. Stević, S., Sharma, A., Krishan, R.: Boundedness and compactness of a new product-type operator from general space to Bloch-type spaces. J. Inequal. Appl. 2016, 219 (2016)

    Article  MathSciNet  Google Scholar 

  22. Tjani, M.: Compact composition operators on some Möbius invariant Banach space. Ph.D. dissertation, Michigan State university (1996)

  23. Zhu, K.: Bloch type spaces of analytic functions. Rocky Mt. J. Math. 23, 1143–1177 (1993)

    Article  MathSciNet  Google Scholar 

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

    Book  Google Scholar 

  25. Zhu, X.: Products of differentiation, composition and multiplication from Bergman type spaces to Bers type space. Integr. Transform. Spec. Funct. 18, 223–231 (2007)

    Article  MathSciNet  Google Scholar 

  26. Zhu, X.: Generalized weighted composition operators on weighted Bergman spaces. Numer. Funct. Anal. Opt. 30, 881–893 (2009)

    Article  MathSciNet  Google Scholar 

  27. Zhu, X.: Generalized weighted composition operators from Bloch spaces into Bers-type spaces. Filomat 26, 1163–1169 (2012)

    Article  MathSciNet  Google Scholar 

  28. Zhu, X.: Generalized weighted composition operators on Bloch-type spaces. J. Inequal. Appl. 2015, 59–68 (2015)

    Article  MathSciNet  Google Scholar 

  29. Zhu, X.: Essential norm of generalized weighted composition operators on Bloch-type spaces. Appl. Math. Comput. 274, 133–142 (2016)

    MathSciNet  MATH  Google Scholar 

  30. Zhu, X.: Generalized weighted composition operators on weighted Bergman spaces, II. Math. Inequal. Appl. 22, 1055–1066 (2019)

    MathSciNet  MATH  Google Scholar 

  31. Zhu, X., Abbasi, E., Ebrahimi, A.: A class of operators related composition operators from the Besov spaces into the Bloch space. Bull. Iran. Math. Soc. (2020). https://doi.org/10.1007/s41980-020-00374-w

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ebrahim Abbasi.

Additional information

Communicated by Mohammad B. Asadi.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Abbasi, E., Zhu, X. Product-Type Operators from the Bloch Space into Zygmund-Type Spaces. Bull. Iran. Math. Soc. 48, 385–400 (2022). https://doi.org/10.1007/s41980-020-00523-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s41980-020-00523-1

Keywords

Mathematics Subject Classification

Navigation