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<p>We consider multifractal Mandelbrot cascades supported on planar <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(C^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> curves with nonvanishing curvature and show that their Fourier dimension is as large as possible, i.e., equal to the infimum of the lower pointwise dimension of the measure.</p>

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Fourier dimension of Mandelbrot cascades on planar curves

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年8月5日

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  • Donggeun Ryou,
  • Ville Suomala

摘要

We consider multifractal Mandelbrot cascades supported on planar \(C^2\) C 2 curves with nonvanishing curvature and show that their Fourier dimension is as large as possible, i.e., equal to the infimum of the lower pointwise dimension of the measure.