Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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BOUNDEDNESS OF THE STRONG MAXIMAL OPERATOR WITH THE HAUSDORFF CONTENT

  • Saito, Hiroki (College of Science and Technology Nihon University)
  • Received : 2018.03.29
  • Accepted : 2018.07.20
  • Published : 2019.03.31
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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.

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References

  1. D. R. Adams, Choquet integrals in potential theory, Publ. Mat. 42 (1998), no. 1, 3-66. https://doi.org/10.5565/PUBLMAT_42198_01
  2. J. Orobitg and J. Verdera, Choquet integrals, Hausdorff content and the Hardy-Littlewood maximal operator, Bull. London Math. Soc. 30 (1998), no. 2, 145-150. https://doi.org/10.1112/S0024609397003688