Boundedness of fractional integral operators on Musielak–Orlicz Hardy spaces

Abstract

AbstractLet and let be Musielak–Orlicz functions such that , are Orlicz functions and , are Muckenhoupt weights. In this paper, we give the necessary and sufficient condition for the boundedness of the fractional integral operator from the Musielak–Orlicz Hardy space into the Musielak–Orlicz Hardy space . We also give the necessary and sufficient condition for the boundedness of from into the Musielak–Orlicz space . Our results generalize the main results in [5, 20, 21].