Weighted norm inequalities for the maximal operator on variable Lebesgue spaces

摘要

We prove weighted strong and weak-type norm inequalities for the Hardy-Littlewood maximal operator on the variable Lebesgue space L ~p({dot operator}). Our results generalize both the classical weighted norm inequalities on L ~p and the more recent results on the boundedness of the maximal operator on variable Lebesgue spaces.