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

Abstract. We shall show that the space of all approximately continuous functions with the topology of pointwise convergence is not homeomorphic to its category analogue.2000 AMS Classification: 54C35, 54C30, 26A15.

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