IDEAS home Printed from https://ideas.repec.org/a/bla/mathna/v299y2026i4p828-862.html

Weighted function spaces: Convolutors, multipliers, and mollifiers

Author

Listed:
  • Lenny Neyt
  • Yoshihiro Sawano

Abstract

We study smooth function spaces of Gelfand–Shilov type, with global behavior governed through a translation‐invariant Banach function space (TIBF) and localized via a weight function system. We clarify the roles of the TIBF, convolution, and pointwise multiplication in connection with the weight function system. Our primary goal is to characterize these function spaces—as well as the corresponding convolutor and multiplier spaces—through mollification. For this purpose, we introduce the moment‐wise decomposition factorization property for pairs of compactly supported smooth functions, and establish complete characterizations in terms of mollifications with these windows.

Suggested Citation

  • Lenny Neyt & Yoshihiro Sawano, 2026. "Weighted function spaces: Convolutors, multipliers, and mollifiers," Mathematische Nachrichten, Wiley Blackwell, vol. 299(4), pages 828-862, April.
    • Handle: RePEc:bla:mathna:v:299:y:2026:i:4:p:828-862
    DOI: 10.1002/mana.70110
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/mana.70110
    Download Restriction: no
    File URL: https://libkey.io/10.1002/mana.70110?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    More about this item

    Statistics

    Access and download statistics

    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:bla:mathna:v:299:y:2026:i:4:p:828-862. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0025-584X .

    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.