Skip to main content
SpringerLink
Log in

On the composition operators on the Bloch space of several complex variables

  • Published:
Science in China Series A: Mathematics Aims and scope Submit manuscript

Abstract

In this paper we first look upon some known results on the composition operator as bounded or compact on the Bloch-type space in polydisk and ball, and then give a sufficient and necessary condition for the composition operator to be compact on the Bloch space in a bounded symmetric domain.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

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. Timoney, R., Bloch function in several complex variables, I, Bull. London Math. Soc., 1980, 12: 241–267.

    Article  MATH  MathSciNet  Google Scholar 

  2. Timoney, R., Bloch function in several Vomplex variables, II, J. Reine Angew Math. 1980, 319: 1–22.

    MATH  MathSciNet  Google Scholar 

  3. Madigan, K., Matheson, A., Compact composition operators on the Bloch space, Trans. Amer. Math. Soc., 1995, 347: 2679–2687.

    Article  MATH  MathSciNet  Google Scholar 

  4. Shi, J. H., Luo, L., Composition operators on the Bloch space of several complex variables, Acta Mathematica Sinica, 2000, 16: 85–98.

    Article  MATH  MathSciNet  Google Scholar 

  5. Zhou, Z. H., Shi, J. H., Compactness of composition operators on the Bloch space in classical bounded symmetric domains, Michigan Math. J., 2002, 50: 381–405.

    Article  MATH  MathSciNet  Google Scholar 

  6. Hua, L. K., Harmonic analysis of functions of several complex variables in the classical domains, Transl. Amer. Math. Soc., 1963, 1: 6.

    Google Scholar 

  7. Lu, Q. K., The Classical Manifolds and the Classical Domains (in Chinese), Shanghai: Shanghai Scientific and Technical Publishers, 1963.

    Google Scholar 

  8. Zhou, Z. H., Shi, J. H., Compact composition operators on the Bloch space in polydiscs, Science in China, Ser. A, 2001, 44: 286–291.

    Article  MATH  MathSciNet  Google Scholar 

  9. Zhou, Z. H., Shi, J. H., Composition operators on the Bloch space in polydiscs, Complex Variables, 2001, 46(1): 73–88.

    MATH  MathSciNet  Google Scholar 

  10. Zhou, Z. H., Composition operators on the Lipschitz space in polydiscs, Science in China, Ser. A, 2003, 46(1): 33–38.

    Article  Google Scholar 

  11. Zhou, Z. H., Shi, J. H., The essential normal of a composition operators on the Bloch space in polydiscs, Chinese Journal of Contemporary Mathematics, 2003, 24(2): 175–186.

    MATH  MathSciNet  Google Scholar 

  12. Zhou, Z. H., Stevo, S., Dana, C., Composition operator between Bloch-type space in polydisc, to appear.

  13. Zhou, Z. H., The essential normal of a composition operators beween the Bloch-type space in polydiscs (to appear).

  14. Zhou, Z. H., Weighted composition operator between Bloch-type space in polydisc (Part of them was reported in ICM2002, Geometry Function in SCV).

  15. Zhou, Z. H., Zeng, H. G., Composition operator p-Bloch space and q-Bloch space in the unit ball, Progress in Natural Science, 2003, 13: 233–236.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Tianjin University, 300072, Tianjin, China

    Zehua Zhou & Renyu Che

  2. LiuHui Center for Applied Mathematics, Nankai University & Tianjin University, 300072, Tianjin, China

    Zehua Zhou & Renyu Che

Authors
  1. Zehua Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Renyu Che
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhou, Z., Che, R. On the composition operators on the Bloch space of several complex variables. Sci. China Ser. A-Math. 48 (Suppl 1), 392–399 (2005). https://doi.org/10.1007/BF02884723

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02884723

Keywords

Search

Navigation