$L^2$-Flattening of Self-similar Measures on Non-degenerate Curves

Amir Algom, Osama Khalil

Let $\hat{I}¼$ be a non-atomic self-similar measure on $\mathbb{R}$, and let $\hat{I}½$ be its pushforward to a non-degenerate curve in ${\mathbb{R}}^d,d\ge 1$. We show that for every $\hat{I}\mu >0$,…