Multiplication Operators on Weighted Grand Lorentz Spaces with Various Properties

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 this study, instead of using rearrangement for a measurable function, weighted Grand Lorentz spaces are defined by using the maximal function 1 ≤ p, q ≤ ∞ where the weight function is measurable, complex valued, and locally bounded. In addition, multiplication operators on weighted grand Lorentz spaces are defined and the fundamental properties of these operators such as boundedness, closed range, invertibility, compactness, and closedness are characterized. © 2023 World Scientific and Engineering Academy and Society. All rights reserved.