IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v7y2019i10p886-d269964.html
   My bibliography  Save this article

Boundedness of Generalized Parametric Marcinkiewicz Integrals Associated to Surfaces

Author

Listed:
  • Mohammed Ali

    (Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid 22110, Jordan)

  • Oqlah Al-Refai

    (Department of Mathematics, Faculty of Science, Taibah University, Almadinah Almunawwarah 41477, Saudi Arabia)

Abstract

In this article, the boundedness of the generalized parametric Marcinkiewicz integral operators M Ω , ϕ , h , ρ ( r ) is considered. Under the condition that Ω is a function in L q ( S n − 1 ) with q ∈ ( 1 , 2 ] , appropriate estimates of the aforementioned operators from Triebel–Lizorkin spaces to L p spaces are obtained. By these estimates and an extrapolation argument, we establish the boundedness of such operators when the kernel function Ω belongs to the block space B q 0 , ν − 1 ( S n − 1 ) or in the space L ( log L ) ν ( S n − 1 ) . Our results represent improvements and extensions of some known results in generalized parametric Marcinkiewicz integrals.

Suggested Citation

  • Mohammed Ali & Oqlah Al-Refai, 2019. "Boundedness of Generalized Parametric Marcinkiewicz Integrals Associated to Surfaces," Mathematics, MDPI, vol. 7(10), pages 1-13, September.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:886-:d:269964
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/7/10/886/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/7/10/886/
    Download Restriction: no
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Mohammed Ali & Hussain Al-Qassem, 2022. "A Note on a Class of Generalized Parabolic Marcinkiewicz Integrals along Surfaces of Revolution," Mathematics, MDPI, vol. 10(20), pages 1-13, October.

    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:7:y:2019:i:10:p:886-:d:269964. 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.