On $L^2$ estimates for quadratic images of product Frostman measures

Sung-Yi Liao, Thang Pham, Chun-Yen Shen

Let $f\in \mathbb{R}[x,y,z]$ be a fixed non-degenerate quadratic polynomial. Given an $\hat{I}\pm$-Frostman probability measure $\hat{I}¼$ supported on $[0,1]$ with $\hat{I}\pm \in (0,1)$, consider the push…