Skip to main content
SpringerLink
Log in

Weighted composition operators between generally weighted Bloch spaces of polydisk

  • Published:
Wuhan University Journal of Natural Sciences

Abstract

Let ϕ be a holomorphic self-map of the open unit polydisk U n in C n and ψ a holomorphic function on U n, p, q > 0. In this paper, we study the generally weighted Bloch space. The growth estimation of functions in such a kind of space is given by the use of the integral method. Using the growth estimation of functions and the function-theoretical properties of those maps ψ and ϕ, sufficient conditions for the weighted composition operator W ψ,ϕ induced by ψ and ϕ to be bounded and compact between the generally weighted Bloch spaces are investigated.

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

Similar content being viewed by others

References

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

    Article  MATH  MathSciNet  Google Scholar 

  2. Contreras M D, Hernandez-Diaz A G. Weighted composition operators in weighted Banach spaces of analytic functions [J]. J Austral Math Soc, 2000, 69A: 41–46.

    Article  MathSciNet  Google Scholar 

  3. Cowen C C, MacCluer B D. Composition Operators on Spaces of Analytic Functions [M]. Boca Roton: CRC Press, 1995.

    Google Scholar 

  4. Zhu K. Spaces of Holomorphic Functions in the Unit Ball [M]. New York: Springer-Verlag, 2005.

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  6. Shi J H. Compactness of composition operators on the bloch space in classical bounded symmetric domains [J]. The Michigan Mathematical Journal, 2002, 50: 381–405.

    Article  MATH  MathSciNet  Google Scholar 

  7. Zhou Zehua, Shi Jihuai. Compact composition operators on the Bloch space in polydisk [J]. Science in China (Series A), 2001, 44(3): 286–291.

    Article  MATH  MathSciNet  Google Scholar 

  8. Zhou Zehua. Composition Operators on the Lipschitz Spaces in Polydisk [J]. Science in China(Series A), 2003, 46(1): 33–38.

    MathSciNet  Google Scholar 

  9. Li Haiying, Zuo Fei. Composition operators between B α space and Q βlog space[J]. Journal of Henan Normal University (Natural Science), 2008, 36(6): 15–17(Ch).

    MathSciNet  Google Scholar 

  10. Ohno S, Strethoff K, Zhao R H. Weighted composition operators between Bloch-type spaces [J]. Rochy Mountain J Math, 2003, 33(1): 191–215.

    Article  MATH  Google Scholar 

  11. Yoneda R. The Composition operator on weighted Bloch space [J]. Arch Math, 2002, 78: 310–317.

    Article  MATH  MathSciNet  Google Scholar 

  12. Li H Y, Liu P D, Wang M F. Composition operators between generally weighted Bloch spaces of polydisk [J]. Journal of Inequalities in Pure and Applied Mathematics, 2007, 8(3): 1–8.

    MathSciNet  Google Scholar 

  13. Li H Y, Liu P D. Composition operators between generally weighted Bloch space and Q βlog space [J]. Banach Journal of Mathematical Analysis, 2009, 3(1): 99–110.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, Henan, China

    Haiying Li

  2. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, Hubei, China

    Peide Liu

Authors
  1. Haiying Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Peide Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Haiying Li.

Additional information

Foundation item: Supported by the National Natural Science Foundation of China (10671147, 10401027),the Key Project of Ministry of Education of China (208081) and the Natural Science Foundation of Henan(2007110016; 2008B110006)

Biography: LI Haiying, female, Associate professor, Ph. D., research direction: functional analysis and its applications.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, H., Liu, P. Weighted composition operators between generally weighted Bloch spaces of polydisk. Wuhan Univ. J. Nat. Sci. 15, 7–12 (2010). https://doi.org/10.1007/s11859-010-0102-3

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11859-010-0102-3

Key words

CLC number

Search

Navigation