Let $T : D(\Omega) \to \mathbb R$, be a generalised function. What can we say about its integrability? For example, does it belong to $L^p(\mathbb R)$? I am interested in the case of non-regular distributions.
This question arose while studying Sobolev spaces. Let $f \in W^{k, p}(\mathbb R)$. So its weak derivatives up to the order $k$ are in $L^p(\mathbb R)$. What does it mean for them to be in $L^p(\mathbb R)$?