Let \(\Lambda \subset \Omega \subset R^ n\) be open sets. The author shows that those distributions on \(\Lambda\) which can be extended to distributions on \(\Omega\), can be characterized as linear continuous functionals over space \({\mathcal P}(\Lambda,\Omega)\) of test functions where \({\mathcal P}(\Lambda,\Omega)\) is the strict inductive limit of a sequence of well known nuclear Fréchet spaces. Using this representation, the space of multiplication operators on \({\mathcal P}(\Lambda,\Omega)\) is calculated, and the space of absolutely regular extendable distributions.