Fourier dimension of Mandelbrot cascades on planar curves

Abstract

We consider multifractal Mandelbrot cascades supported on planar $C^2$ 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.

19 pages, incorporated referee comments, updated a reference, to appear in Probab. Theory Related Fields

References in corpus (1)

• Near-optimal restriction estimates for Cantor sets on the parabola