Fourier dimension of Mandelbrot multiplicative cascades

Changhao Chen, Bing Li, Ville Suomala

We investigate the Fourier dimension, ${\dim }_F\hat{I}¼$, of Mandelbrot multiplicative cascade measures $\hat{I}¼$ on the $d$-dimensional unit cube. We show that if $\hat{I}¼$ is the cascade measure g…