Skip to main content
SpringerLink
Log in

Essential Norms of Weighted Composition Operators on \(\mathcal {N}_{p}\)-Spaces in the Ball

  • Published:
Vietnam Journal of Mathematics Aims and scope Submit manuscript

Abstract

We obtain the estimate for the essential norms of weighted composition operators acting from \(\mathcal {N}_{p}\)-spaces into the Beurling/Bergman-type spaces A −q of holomorphic functions in the unit ball. Our results contain the results in the unit disk as particular cases.

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. Cowen, C., MacCluer, B.: Composition Operators on Spaces of Analytic Functions. CRC Press, Florida (1995)

    MATH  Google Scholar 

  2. Duren, P., Weir, R.: The pseudohyperbolic metric and Bergman spaces in the ball. Trans. Am. Math. Soc. 359, 63–76 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  3. Hedenmalm, H., Korenblum, B., Zhu, K.: Theory of Bergman Spaces. Springer, New York (2000)

    Book  MATH  Google Scholar 

  4. Hu, B., Khoi, L.H.: Weighted-composition operators on \(\mathcal {N}_{p}\)-spaces in the ball. Comptes Rendus Math. 351, 719–723 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  5. Hu, B., Khoi, L.H.: Compact difference of weighted composition operators on \(\mathcal {N}_{p}\)-spaces in the ball. Rom. J. Pure Appl. Math. LX, 101–116 (2015)

    MathSciNet  Google Scholar 

  6. Palmberg, N.: Composition operators acting on \(\mathcal {N}_{p}\)-spaces. Bull. Belg. Math. Soc. 14, 545–554 (2007)

    MathSciNet  MATH  Google Scholar 

  7. Rudin, W.: Function Theory in the Unit Ball of \(\mathbb {C}^{n}\). Springer, New York (1980)

    Book  Google Scholar 

  8. Shapiro, J.H.: Compositions Operators and Classical Function Theory. Springer, New York (1993)

    Book  Google Scholar 

  9. Ueki, S.: Weighted composition operators acting between the \(\mathcal {N}_{p}\)-space and the weighted-type space \(H_{\alpha }^{\infty }\). Indag. Math. 23, 243–255 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  10. Zhu, K.: Spaces of Holomorphic Functions in the Unit Ball. Springer (2004)

Download references

Acknowledgments

The authors would like to thank the referees for several suggestions that improved the presentation of the paper.

Author information

Authors and Affiliations

  1. Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University (NTU), Singapore, 637371, Singapore

    Hu Bingyang & Le Hai Khoi

  2. Department of Mathematics and Statistics, Mail Stop 942, University of Toledo, Toledo, OH, 43606, USA

    Trieu Le

Authors
  1. Hu Bingyang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Le Hai Khoi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Trieu Le
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Le Hai Khoi.

Additional information

Hu Bingyang and Le Hai Khoi are supported in part by MOEs AcRF Tier 1 grant M4011166.110 (RG24/13).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bingyang, H., Khoi, L.H. & Le, T. Essential Norms of Weighted Composition Operators on \(\mathcal {N}_{p}\)-Spaces in the Ball. Vietnam J. Math. 44, 431–439 (2016). https://doi.org/10.1007/s10013-015-0177-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10013-015-0177-4

Keywords

Mathematics Subject Classification (2010)

Search

Navigation