Ilker Eryilmaz, Gokhan Isik, "Banach Function Space Property of A New Type of Grand Lorentz Spaces," WSEAS Transactions on Mathematics, vol. 22, pp. 348-353, 2023, DOI:10.37394/23206.2023.22.41
Ilker Eryilmaz, Gokhan Isik. Banach Function Space Property of A New Type of Grand Lorentz Spaces.
WSEAS Transactions on Mathematics. 2023;22:348-353. 10.37394/23206.2023.22.41
WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 22, 2023
Banach Function Space Property of A New Type of Grand Lorentz Spaces
Authors: ,
Abstract: The concept of Lorentz space has been generalized to the grand Lorentz space. In this paper, a new generalization of Lorentz spaces are defined as $$L^{(p,q)} (Χ,Σ,μ)$$ with $$θ\geq0$$ by using 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 a proof which can serve as a reference for next studies and literature and as fundamental reference for subsequent results.
Pages: 348-353 WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 22, 2023, Art. #41 DOI: 10.37394/23206.2023.22.41
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