On Fourier transforms of fractal measures on the parabola

Tuomas Orponen, Carmelo Puliatti, Aleksi Pyörälä

Let $s\in [0,1]$ and $t\in [0,\min \{3s,s+1\})$. Let $\ddot{I}ƒ$ be a Borel measure supported on the parabola $\mathbb{P}=\{(x,x^2):x\in [-1,1]\}$ satisfying the $s$-dimensional…