Boundedness of the strong maximal operator with the Hausdorff content
Bull. Korean Math. Soc.
Published online 2018 Sep 07
Hiroki Saito
Nihon University
Abstract : Let $n$ be the spatial dimension.
For $d,0<d\le n$,
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 : 42B25
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