Some remarks on the Hardy-Littlewood maximal function on variable Lp spaces
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- Lerner, A. Math. Z. (2005) 251: 509. doi:10.1007/s00209-005-0818-5
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We show that any pointwise multiplier for BMO(ℝn) generates a function p from the class (ℝn) of those functions for which the Hardy-Littlewood maximal operator is bounded on the variable Lp space. In particular, this gives a positive answer to Diening's conjecture saying that there are discontinuous functions which nevertheless belong to (ℝn).