In the present paper, we shall give necessary and sufficient conditions for the strong and weak boundedness of the Riesz potential operator I-alpha on Orlicz spaces. Cianchi (J. Lond. Math. Soc. 60(1): 247-286, 2011) found ...

In this paper, we find necessary and sufficient conditions for the boundedness of fractional maximal operator M on Orlicz spaces. As an application of this results we consider the boundedness of fractional maximal commutator ...