Fourier dimension of Mandelbrot cascades on planar curves

• 成果类型: Article; Early Access
• 署名作者: Ryou, Donggeun; Suomala, Ville
• 署名单位: Indiana University System; Indiana University Bloomington; University of Oulu
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051; 1432-2064
• DOI: 10.1007/s00440-026-01528-3
• 发表日期: 2026-08-05
• 关键词: Fourier dimension; Mandelbrot cascades; planar curves; martingales; spectrum

摘要

We consider multifractal Mandelbrot cascades supported on planar C2 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.