Our aim in this paper is to deal with the boundedness of the Hardy- Littlewood maximal operator and the Hardy operator on non-homogeneous central Herz-Morrey-Musielak-Orlicz spaces and to establish a generalization of Sobolev’s inequalities for Riesz potentials of functions in such spaces.
The third author is supported by Grant-in-Aid for Scientific
Research(C), No. 19K03586.
We would like to express our thanks to the referee for his/her comments.
"Boundedness of maximal operator, Hardy operator and Sobolev’s inequalities on non-homogeneous central Herz-Morrey-Musielak-Orlicz spaces." Hiroshima Math. J. 51 (1) 13 - 55, March 2021. https://doi.org/10.32917/h2019141