  In our companion paper (S.N. Chandler Wilde, D.P. Hewett, A. Moiola, Sobolev
spaces on non-Lipschitz subsets of $\mathbb{R}^n$ with application to boundary
integral equations on fractal screens, 2016) we studied a number of different
Sobolev spaces on a general (non-Lipschitz) open subset $\Omega$ of
$\mathbb{R}^n$, defined as closed subspaces of the classical Bessel potential
spaces $H^s(\mathbb{R}^n)$ for $s\in\mathbb{R}$. These spaces are mapped by the
restriction operator to certain spaces of distributions on $\Omega$. In this
note we make some observations about the relation between these spaces of
global and local distributions. In particular, we study conditions under which
the restriction operator is or is not injective, surjective and isometric
between given pairs of spaces. We also provide an explicit formula for minimal
norm extension (an inverse of the restriction operator in appropriate spaces)
in a special case.
