Orlicz-fractional maximal operators in Morrey and Orlicz–Morrey spaces

Abstract

In 1995, Perez introduced $$B_{p}$$ -condition, which is necessary and sufficient condition for the boundedness of the Orlicz maximal operator on $$L^{p}$$ spaces. After, necessary and sufficient condition of the Hardy–Littlewood–Sobolev type inequality for Orlicz-fractional maximal operator is derived by Cruz-Uribe and Moen in 2013. In this paper, we investigate the boundedness of Orlicz maximal operator, Orlicz-fractional maximal operator and fractional integral operator in Morrey and Orlicz–Morrey spaces on the assumption that each Young function satisfies these conditions, respectively. In particular, one of the main results is based on the Adams inequality in the framework of Morrey spaces.