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

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. © 2023 World Scientific and Engineering Academy and Society. All rights reserved.