Banach Function Space Property of A New Type of Grand Lorentz Spaces

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Eryılmaz İ., Isik G.

WSEAS Transactions on Mathematics, vol.22, pp.348-353, 2023 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 22
  • Publication Date: 2023
  • Doi Number: 10.37394/23206.2023.22.41
  • Journal Name: WSEAS Transactions on Mathematics
  • Journal Indexes: Scopus, INSPEC, zbMATH
  • Page Numbers: pp.348-353
  • Keywords: Banach function space, Distribution function, Grand Lorentz space, Iwaniec-Sbordone space
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

The concept of Lorentz space has been generalized to the grand Lorentz space. In this paper, a new generalization of Lorentz spaces is defined as Lo p, q) ( X, E, μ ) with p > 0 by using the maximal function of a measurable function. Besides an explicit proof of being Banach function space with a rearrangement invariant norm seemed to be missing in the literature. Therefore, the authors provided such proof which can serve as a reference for the next studies and literature and as a fundamental reference for subsequent results.