논문KCI 등재
Boundedness of the strong maximal operator with the Hausdorff content
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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 $L^{p}(H^{d},\R^n)$ for $\min(1,d)<p$. We also show that our result is sharp.
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 $L^{p}(H^{d},\R^n)$ for $\min(1,d)<p$. We also show that our result is sharp.
참고문헌 (2)
- D. R. Adams, "Choquet integrals in potential theory", Publ. Mat, 42(1), pp.3~66 (1998)
- J. Orobitg, "Choquet integrals, Hausdorff content and the Hardy-Littlewood maximal operator", Bull. London Math. Soc, 30(2), pp.145~150 (1998)
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