Affiliation:
1. Department of Mathematics, Faculty of Sciences, Ondokuz Mayıs University, Kurupelit-Atakum, Samsun, TURKEY
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.
Publisher
World Scientific and Engineering Academy and Society (WSEAS)
Reference30 articles.
1. S.C.Arora, G.Datt and S.Verma, Multiplication operators on Lorentz spaces, Indian J. Math., 48-3, 2006, 317-329.
2. S.C. Arora, G. Datt and S.Verma, Weighted composition operators on Lorentz spaces, Bull. Korean Math. Soc., 44-4, 2007, 701-708.
3. S.C. Arora, G. Datt and S.Verma, Composition Operators on Lorentz spaces, Bull. Austral. Math. Soc., 76, 2007, 205-214.
4. R.E. Castillo, H. Rafeiro, An introductory course in Lebesgue spaces, CMS Books in Mathematics/Ouvrages de Mathematiques de la SMC. Springer, [Cham], 2016. xii+461 pp.
5. J.T. Chan, A note on compact weighted composition operators on L p , Acta Sci. Math. (Szeged), 56-2, 1992, 165-168.