Skip to main content
SpringerLink
Log in

Meromorphic Bergman Spaces

  • Published:
Ukrainian Mathematical Journal Aims and scope

We introduce new spaces of holomorphic functions on the pointed unit disc in ℂ generalizing the classical Bergman spaces. We prove some fundamental properties of these spaces and their dual spaces. Finally, we extend the Hardy–Littlewood and Fej–Riesz inequalities to these spaces with the use of Toeplitz operators.

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. V. V. Andreev, “Fejér–Riesz type inequalities for Bergman spaces,” Rend. Circ. Mat. Palermo (2), 61, 385–392 (2012).

    Article  MATH  Google Scholar 

  2. P. L. Duren, Theory of Hp Spaces, Academic Press, New-York–London (1970).

  3. H. Hedenmalm, B. Korenblum, and K. Zhu, “Theory of Bergman spaces,” Graduate Texts in Mathematics, 199, Springer-Verlag, New York (2000).

    MATH  Google Scholar 

  4. H. Kim, “On the localization of the minimum integral related to the weighted Bergman kernel and its application,” C. R. Math. Acad. Sci. Paris, 355, 420–425 (2017).

    Article  MathSciNet  MATH  Google Scholar 

  5. S. G. Krantz, “Geometric analysis of the Bergman kernel and metric,” Graduate Texts in Mathematics, 268, Springer, New York (2013).

    Book  Google Scholar 

  6. P. Sobolewski, “Inequalities on Bergman spaces,” Ann. Univ. Mariae Curie-Skłodowska Sect. A, 61, 137–143 (2007).

    MathSciNet  MATH  Google Scholar 

  7. K. Zhu, “Translating inequalities between Hardy and Bergman spaces,” Amer. Math. Monthly, 111, 520–525 (2004).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Gabes, Faculty of Sciences of Gabes, Gabes, Tunisia

    N. Ghiloufi

  2. Shaqra University, Shaqra, Saudi Arabia

    M. Zaway

  3. Irescomath Laboratory, Gabes University, Gabes, Tunisia

    M. Zaway

Authors
  1. N. Ghiloufi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Zaway
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. Ghiloufi.

Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 8, pp. 1060–1072, August, 2022. Ukrainian https://doi.org/10.37863/umzh.v74i8.6163.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ghiloufi, N., Zaway, M. Meromorphic Bergman Spaces. Ukr Math J 74, 1209–1224 (2023). https://doi.org/10.1007/s11253-023-02130-9

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-023-02130-9

Search

Navigation