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

Creative Commons License

Eryılmaz İ., Isik G.

WSEAS Transactions on Mathematics, cilt.22, ss.348-353, 2023 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 22
  • Basım Tarihi: 2023
  • Doi Numarası: 10.37394/23206.2023.22.41
  • Dergi Adı: WSEAS Transactions on Mathematics
  • Derginin Tarandığı İndeksler: Scopus, INSPEC, zbMATH
  • Sayfa Sayıları: ss.348-353
  • Anahtar Kelimeler: Banach function space, Distribution function, Grand Lorentz space, Iwaniec-Sbordone space
  • Ondokuz Mayıs Üniversitesi Adresli: Evet

Özet

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.