Some New Results on Weighted Grand Lorentz Spaces

Abstract

The concept of Lebesgue space has been generalized to the grand Lebesgue space with non-weight and weight, and the classical Lorentz space concept has been generalized to grand Lorentz spaces with a similar logic in literature. In this study, instead of using rearrangement function of a measurable function, weighted grand Lorentz spaces are defined by using the maximal function for 1 <= p, q <= infinity. In addition, being Banach function space and some inclusion properties in weighted grand Lorentz spaces are investigated.