Bulletin of the
Korean Mathematical Society BKMS

Let $n$ be the spatial dimension. For $d$, $ 0 < d \leq n$, let $H^{d}$ be the $d$-dimensional Hausdorff content. The purpose of this paper is to prove the boundedness of the dyadic strong maximal operator on the Choquet space $L^{p}(H^{d},\mathbb R^n)$ for $\min(1,d) < p$. We also show that our result is sharp.

Keywords: strong maximal operator, Hausdorff content

MSC numbers: Primary 42B25; Secondary 42B35

Supported by: The author is supported by Grant-in-Aid for Young Scientists (B) (15K17551), the Japan Society for the Promotion of Science.