Maximal function on generalized Lebesgue spaces L^p(⋅)

We prove the boundedness of the Hardy-Littlewood maximal function on the generalized Lebesgue space L p() (R d ) under a continuity assumption on p that is weaker than uniform Hlder continuity. We deduce continuity of mollifying sequences and density of C () in W 1,p() () .

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