Endpoint estimates for commutators with respect to the fractional integral operators on Orlicz–Morrey spaces

Abstract

It is known that the necessary and sufficient conditions of the boundedness of commutators on Morrey spaces are given by Di Fazio, Ragusa and Shirai. Moreover, according to the result of Cruz-Uribe and Fiorenza in 2003, it is given that the weak-type boundedness of the commutators of the fractional integral operators on the Orlicz spaces as the endpoint estimates. In this paper, we gave the extention to the weak-type boundedness on the Orlicz–Morrey spaces.