Abstract dyadic cubes, maximal operators and Hausdorff content

作者：Saito Hiroki^*; Tanaka Hitoshi; Watanabe Toshikazu

来源：Bulletin des Sciences Mathematiques, 2016, 140(6): 757-773.

DOI：10.1016/j.bulsci.2016.02.001

• Abstract dyadic cubes
• Dyadic Hausdorff content
• Choquet integral
• Maximal operator

Let it be a locally finite Borel measure and 2) a family of measurable sets equipped with a certain dyadic structure. For E subset of R-n and 0 < a <= n, by alpha-dimensional Hausdorff content we mean
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where the infimum is taken over all coverings of E by countable families of the abstract dyadic cubes {Q(j)} subset of D. In this paper we study the boundedness of the Hardy-Littlewood maximal operator M-D(mu) adapted to D and mu, that is, we prove the strong type (p, p) inequality
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where the integrals are taken in the Choquet sense.

• 出版日期2016-9