Semialgebraic Calderon-Zygmund theorem on regularization of the distance function

Beata Kocel-Cynk, Wiesław Pawłucki, Anna Valette

We prove that, for any closed semialgebraic subset $W$ of ${\mathbb{R}}^n$ and for any positive integer $p$, there exists a Nash function $f:\mathbb{R}^n\setminus W\longrightarrow (0…