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(ℝn) generates a function p from the class P(ℝn) 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 P(ℝn).

Original languageEnglish
Pages (from-to)509-521
Number of pages13
JournalMathematische Zeitschrift
Volume251
Issue number3
DOIs
StatePublished - Nov 2005

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