Spherical means and measures with finite energy
We prove a restricted weak type inequality for the spherical means operator with respect to measures with finite α-energy, α ≤ 1. This complements recent results due to D. Oberlin.
On Nikodym-type sets in high dimensions
We prove that the complement of a higher-dimensional Nikodym set must have full Hausdorff dimension.
(n,2)-sets have full Hausdorff dimension.
We prove that a set containing translates of every 2-plane must have full Hausdorff dimension.
Corrigendum to .
In the paper , appeared in Rev. Mat. Iberoamericana 20 (2004), 381-393, the author claimed that an (n,2)-set must have full Hausdorff dimension. However, as pointed out by Terence Tao and John Bueti, the proof contains an error.
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