On Kakeya’s maximal function II: high dimensional cases

In this paper an estimate of the Kakeya maximal operator on the high dimensional Euclidean spaces is given, that is, the Kakeya maximal operator is of restricted weak type $(d/(d-1), d/(d-1))$ for the Lebesgue space Ld/(d-1)(Rᵈ), d≥ 2 with the norm bounded by a constant times (log N)1/d.