Maximal and Calderón–Zygmund operators on the local variable Morrey–Lorentz spaces and some applications

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Kucukaslan A., Guliyev V. S., Aykol C., Serbetci A.

Applicable Analysis, vol.102, no.2, pp.406-415, 2023 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 102 Issue: 2
  • Publication Date: 2023
  • Doi Number: 10.1080/00036811.2021.1952995
  • Journal Name: Applicable Analysis
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Computer & Applied Sciences, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.406-415
  • Keywords: Local variable Morrey-Lorentz space, Hardy-Littlewood maximal function, Calderon-Zygmund operators, BOUNDEDNESS, EXPONENT, LEBESGUE
  • Ankara University Affiliated: Yes

Abstract

In this paper, we give the definition of local variable Morrey–Lorentz spaces (Formula presented.) which are a new class of functions. Also, we prove the boundedness of the Hardy–Littlewood maximal operator M and Calderón–Zygmund operators T on these spaces. Finally, we apply these results to the Bochner–Riesz operator (Formula presented.), identity approximation (Formula presented.) and the Marcinkiewicz operator (Formula presented.) on the spaces (Formula presented.).