, Volume 251, Issue 3, pp 509-521
Date: 13 Jul 2005

Some remarks on the Hardy-Littlewood maximal function on variable L p spaces

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Abstract

We show that any pointwise multiplier for BMO(ℝ n ) generates a function p from the class (ℝ n ) of those functions for which the Hardy-Littlewood maximal operator is bounded on the variable L p space. In particular, this gives a positive answer to Diening's conjecture saying that there are discontinuous functions which nevertheless belong to (ℝ n ).