An exact local distributional extension test

This section supplies the estimate that must be checked for the coefficients in Section sec:coefficients.

For an open $X\subset {\mathbb{R}}^d$ and $\varphi \in \mathcal{D}(X)$, extend $\varphi$ by zero outside $X$ and set

For a compact $K\subset X$, tests with support in $K$ are understood to have the usual test-function topology.