IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i19p4138-d1251912.html
   My bibliography  Save this article

Sobolev Estimates for the ∂ ¯ and the ∂ ¯ -Neumann Operator on Pseudoconvex Manifolds

Author

Listed:
  • Haroun Doud Soliman Adam

    (Department of Basic Sciences, Deanship of the Preparatory Year, Najran University, P.O. Box 1988, Najran 55461, Saudi Arabia
    These authors contributed equally to this work.)

  • Khalid Ibrahim Adam Ahmed

    (Department of Basic Sciences, Deanship of the Preparatory Year, Najran University, P.O. Box 1988, Najran 55461, Saudi Arabia
    These authors contributed equally to this work.)

  • Sayed Saber

    (Department of Mathematics and Statistics, Faculty of Science, Beni-Suef University, Beni-Suef 62511, Egypt
    Department of Mathematics, Al-Baha University, Baljurashi 65799, Saudi Arabia
    These authors contributed equally to this work.)

  • Marin Marin

    (Department of Mathematics and Computer Science, Transilvania University of Brasov, 500036 Brasov, Romania
    Academy of Romanian Scientists, Ilfov Street, No. 3, 050045 Bucharest, Romania
    These authors contributed equally to this work.)

Abstract

Let D be a relatively compact domain in an n -dimensional Kähler manifold with a C 2 smooth boundary that satisfies some “Hartogs-pseudoconvexity” condition. Assume that Ξ is a positive holomorphic line bundle over X whose curvature form Θ satisfies Θ ≥ C ω , where C > 0 . Then, the ∂ ¯ -Neumann operator N and the Bergman projection P are exactly regular in the Sobolev space W m ( D , Ξ ) for some m , as well as the operators ∂ ¯ N , ∂ ¯ ⋇ N .

Suggested Citation

  • Haroun Doud Soliman Adam & Khalid Ibrahim Adam Ahmed & Sayed Saber & Marin Marin, 2023. "Sobolev Estimates for the ∂ ¯ and the ∂ ¯ -Neumann Operator on Pseudoconvex Manifolds," Mathematics, MDPI, vol. 11(19), pages 1-26, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:19:p:4138-:d:1251912
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/19/4138/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/19/4138/
    Download Restriction: no
    ---><---

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:19:p:4138-:d:1251912. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.