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arXiv · 2505.21217

Frostman and Fourier characterisations of fractal dimensions

Kenneth J. Falconer·Shuqin Zhang
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Abstract

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.

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Kenneth J. Falconer, Shuqin Zhang. 2025-05-27. Frostman and Fourier characterisations of fractal dimensions. https://arxiv.org/abs/2505.21217

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