Frostman and Fourier characterisations of fractal dimensions

Kenneth J. Falconer; Shuqin Zhang

doi:10.1007/s00209-026-03961-5

Frostman and Fourier characterisations of fractal dimensions

Kenneth J. Falconer^*, Shuqin Zhang

^*Corresponding author for this work

Pure Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	79
Number of pages	21
Journal	Mathematische Zeitschrift
Volume	312
Issue number	3
Early online date	18 Feb 2026
DOIs	https://doi.org/10.1007/s00209-026-03961-5
Publication status	Published - 1 Mar 2026

Access to Document

10.1007/s00209-026-03961-5Licence: CC BY

Falconer_2026_MZ_Frostman-Fourier-characterisations-fractal_CC
© The Author(s) 2026. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
Final published version, 366 KBLicence: CC BY

https://arxiv.org/abs/2505.21217Licence: CC BY

Cite this

@article{c85fd142be7648b6bbc58a30c86ba37a,

title = "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.",

author = "Falconer, \{Kenneth J.\} and Shuqin Zhang",

note = "Funding: SZ has been supported by the New Cornerstone Science Foundation through the New Cornerstone Investigator Program.",

year = "2026",

month = mar,

day = "1",

doi = "10.1007/s00209-026-03961-5",

language = "English",

volume = "312",

journal = "Mathematische Zeitschrift",

issn = "0025-5874",

publisher = "Springer",

number = "3",

}

TY - JOUR

T1 - Frostman and Fourier characterisations of fractal dimensions

AU - Falconer, Kenneth J.

AU - Zhang, Shuqin

N1 - Funding: SZ has been supported by the New Cornerstone Science Foundation through the New Cornerstone Investigator Program.

PY - 2026/3/1

Y1 - 2026/3/1

N2 - 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.

AB - 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.

U2 - 10.1007/s00209-026-03961-5

DO - 10.1007/s00209-026-03961-5

M3 - Article

SN - 0025-5874

VL - 312

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

IS - 3

M1 - 79

ER -

Frostman and Fourier characterisations of fractal dimensions

Abstract

Access to Document

Fingerprint

Cite this