On the Fourier decay of multiplicative convolutions

Tuomas Orponen, Nicolas de Saxcé, Pablo Shmerkin

We prove the following. Let ${\mu }_1,\dots ,{\mu }_n$ be Borel probability measures on $[-1,1]$ such that ${\mu }_j$ has finite $s_j$-energy for certain indices $s_j\in (0,1]$ with $s_{…