Some remarks on the Hardy-Littlewood maximal function on variable Lp spaces
- First Online:
- 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).