Frostman and Fourier characterisations of fractal dimensions

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.

Authors

Shuqin Zhang
Kenneth J. Falconer

Publication Details

Journal: Mathematische Zeitschrift
Published: 2026-02-18
DOI: https://doi.org/10.1007/s00209-026-03961-5
Primary Topic: Mathematical Dynamics and Fractals
Type: article
Field-Weighted Citation Impact: 0.00

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article

Frostman and Fourier characterisations of fractal dimensions

Shuqin Zhang, Kenneth J. Falconer

Feb 18, 2026

Mathematische Zeitschrift

Mathematical Dynamics and Fractals

article

Frostman and Fourier characterisations of fractal dimensions

Shuqin Zhang, Kenneth J. Falconer

February 18, 2026article en

Abstract

Mathematische ZeitschriftVol. 312(3)

Reduced inequalities

Openalex Percentile: Top 46%

Mathematical Dynamics and Fractals

DOI Open Access PDF OpenAlex

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Frostman and Fourier characterisations of fractal dimensions — Shuqin Zhang, Kenneth J. Falconer · Mathematische Zeitschrift (2026) | TGRS Research Map | TGRS