A Bounded Linear Extension Operator for $L^{2,p}({\mathbb{R}}^2)$

Arie Israel

For a finite $E\subset {\mathbb{R}}^2$, $f:E\to \mathbb{R}$, and $p>2$, we produce a continuous $F:{\mathbb{R}}^2\to \mathbb{R}$ depending linearly on $f$, taking the same values as $f$ on $E$, and…