Boundedness of fractional sublinear operators on weighted grand Herz-Morrey spaces with variable exponents

Abstract This article aims to delve deeper into the weighted grand variable Herz-Morrey spaces, and try to establish the boundedness of fractional sublinear operators and their multilinear commutators within this framework. The results are still new even in the unweighted setting, extending previous research. As applications, the corresponding boundedness estimates for the commutators of maximal operator and Riesz potential operator are established.