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<p>We examine Frostman-type characterisations and other extremal measure criteria for a range of fractal dimensions of sets. In particular we derive properties of the less familiar modified lower box dimension and upper correlation dimension. We also express a number of fractal dimensions in terms of Fourier properties of measures.</p>

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Frostman and Fourier characterisations of fractal dimensions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月18日

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  • Kenneth J. Falconer,
  • Shuqin Zhang

摘要

We examine Frostman-type characterisations and other extremal measure criteria for a range of fractal dimensions of sets. In particular we derive properties of the less familiar modified lower box dimension and upper correlation dimension. We also express a number of fractal dimensions in terms of Fourier properties of measures.