Sufficient condition for boundedness of maximal operator on weighted generalized Orlicz spaces

Abstract

We prove that the Hardy-Littlewood maximal operator is bounded in the weighted generalized Orlicz space if the weight satisfies the classical Muckenhoupt condition $A_p$ and $t\to \frac{\ddot{I}†(x,t)}{t^p}$ is almost increasing in addition to the standard conditions.

12 pages