Mathematische Zeitschrift

, Volume 251, Issue 3, pp 509–521

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

Article

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

Abstract

We show that any pointwise multiplier for BMO(ℝn) generates a function p from the class https://static-content.springer.com/image/art%3A10.1007%2Fs00209-005-0818-5/MediaObjects/s00209-005-0818-5flb1.gif(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 https://static-content.springer.com/image/art%3A10.1007%2Fs00209-005-0818-5/MediaObjects/s00209-005-0818-5flb1.gif(ℝn).

Mathematics Subject Classification (2000)

42B25

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Department of MathematicsBar-Ilan UniversityRamat GanIsrael