3 problems

Let $\mu$ be a codimension-one Ahlfors regular measure on parabolic space $\mathbb R^{n+1}$. Suppose that the parabolic Riesz transform is bounded on $L^2(\mu)$, and that $\mu$ sat…

David–Semmes' conjecture. For Ahlfors regular sets, the PBP and BPLG conditions are equivalent. This conjecture concerns the equivalence of a projection condition with a strong qua…

Let $\Omega^+$ be a proper open set in $\mathbb{R}^2$, let $\Gamma=\partial\Omega^+$, and set $\Omega^- = \mathbb{R}^2\setminus\overline{\Omega^+}$. For $x\in\mathbb{R}^2$ and…