Mathematische Zeitschrift

, Volume 251, Issue 3, pp 509–521

Some remarks on the Hardy-Littlewood maximal function on variable Lp spaces


DOI: 10.1007/s00209-005-0818-5

Cite this article as:
Lerner, A. Math. Z. (2005) 251: 509. doi:10.1007/s00209-005-0818-5


We show that any pointwise multiplier for BMO(ℝn) generates a function p from the class Open image in new window(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 Open image in new window(ℝn).

Mathematics Subject Classification (2000)


Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Department of MathematicsBar-Ilan UniversityRamat GanIsrael

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