Maximal Operator with Rough Kernel in Variable Musielak–Morrey–Orlicz type Spaces, Variable Herz Spaces and Grand Variable Lebesgue Spaces

In the frameworks of some non-standard function spaces (viz. Musielak–Orlicz spaces, generalized Orlicz–Morrey spaces, generalized variable Morrey spaces and variable Herz spaces) we prove the boundedness of the maximal operator with rough kernel. The results are new even for p constant.