Skip to main content
SpringerLink
Log in

Reproducing Kernels of Some Weighted Bergman Spaces

  • Published:
The Journal of Geometric Analysis Aims and scope Submit manuscript

Abstract

Herein, the theory of Bergman kernel is developed to the weighted case. A general form of weighted Bergman reproducing kernel is obtained, by which we can calculate concrete Bergman kernel functions for specific weights and domains.

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. Bekoll, D., Bonami, A., Peloso, M.M., Ricci, F.: Boundedness of Bergman projections on tube domains over light cones. Math. Zeitsch. 237, 31–59 (2001)

    Article  MathSciNet  Google Scholar 

  2. Békollé, D., Bonami, A., Garrigós, G., Nana, C., Peloso, M.M., Ricci, F.: Lecture notes on Bergman projectors in tube domains over cones: an analytic and geometric viewpoint, IMHOTEP 5(2012)

  3. Bergman, S.: The Kernel Function and Conformal Mapping (Mathematical Surveys Number V). American Mathematical Society, Providence (1950)

    Book  Google Scholar 

  4. Boas, H.P., Fu, S., Sreaube, E.J.: The Bergman kernel function: explicit formulas and zeros. Proc. Am. Math. Soc. 127, 805–811 (1999)

    Article  Google Scholar 

  5. Duren, P., Schuster, A.: Bergman Spaces. Mathematical Surveys and Monographs. AMS, Providence (2014)

    MATH  Google Scholar 

  6. Hua, L.: Harmonic Analysis of Functions of Several Complex Variables in the Classical Domains. American Mathematics Society, Providence (1963)

    Book  Google Scholar 

  7. Krantz, S.G.: Function Theory of Several Complex Variables. American Mathematical Society, Providence (2001)

    Book  Google Scholar 

  8. Krantz, S.G.: Geometric Analysis of Bergman kernel and Metric, Graduate Texts in Mathematics 268. Springer, New York (2013)

    Book  Google Scholar 

  9. Saitoh, S.: Integral Transforms, Reproducing Kernels and Their Applications. Pitman Research Notes in Mathematics Series, vol. 369. Addison Wesley Longman, Harlow (1997)

    MATH  Google Scholar 

Download references

Acknowledgements

G-T. Deng: This work was partially supported by NSFC (Grant Nos. 11971042, 11971045 and 12071035) and by SRFDP (Grant 20100003110004). T. Qian: The work is supported by the Macau Science and Technology foundation No.FDCT079/2016/A2, FDCT0123/2018/A3, and the Multi-Year Research Grants of the University of Macau No. MYRG2018-00168-FST.

Author information

Authors and Affiliations

  1. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

    Guan-Tie Deng

  2. Department of Mathematics, Faculty of Science and Technology, University of Macau, Macao (Via Hong Kong), China

    Yun Huang

  3. Institute of Systems Engineering, Macau University of Science and Technology, Avenida Wai Long, Taipa, Macao, China

    Tao Qian

Authors
  1. Guan-Tie Deng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yun Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tao Qian
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yun Huang.

Additional information

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

Deng, GT., Huang, Y. & Qian, T. Reproducing Kernels of Some Weighted Bergman Spaces. J Geom Anal 31, 9527–9550 (2021). https://doi.org/10.1007/s12220-021-00616-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12220-021-00616-1

Keywords

Search

Navigation