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

Andrei K. Lerner

doi:10.1007/s00209-005-0818-5

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

Andrei K. Lerner

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

68 Scopus citations

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 language	English
Pages (from-to)	509-521
Number of pages	13
Journal	Mathematische Zeitschrift
Volume	251
Issue number	3
DOIs	https://doi.org/10.1007/s00209-005-0818-5
State	Published - Nov 2005

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

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