Boundedness of the strong maximal operator with the Hausdorff content
Bull. Korean Math. Soc. 2019 Vol. 56, No. 2, 399-406
Published online March 1, 2019
Hiroki Saito
Nihon University
Abstract : 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
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