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.