Boundedness of maximal operators and Sobolevʼs inequality on Musielak–Orlicz–Morrey spaces

Our aim in this paper is to deal with the boundedness of the Hardy–Littlewood maximal operator on Musielak–Orlicz–Morrey spaces. As an application of the boundedness of the maximal operator, we establish a generalization of Sobolevʼs inequality for general potentials of functions in Musielak–Orlicz–Morrey spaces.