Abstract
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 $L^{d/(d-1)}(\mathbf{R}^{d}), d\geq 2$ with the norm bounded by a constant times $(\log N)^{1/d}$.
Citation
Satoru Igari. "On Kakeya’s maximal function II: high dimensional cases." Proc. Japan Acad. Ser. A Math. Sci. 100 (2) 12 - 15, February 2024. https://doi.org/10.3792/pjaa.100.003
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