Weighted norm inequalities for the maximal operator on variable Lebesgue spaces

We prove weighted strong and weak-type norm inequalities for the Hardy–Littlewood maximal operator on the variable Lebesgue space Lp(⋅)Lp(⋅). Our results generalize both the classical weighted norm inequalities on LpLp and the more recent results on the boundedness of the maximal operator on variable Lebesgue spaces.