I am looking for references on the topic of Sobolev spaces based on $L^p$ with $0<p<1$. For instance, a natural question could be: let $u$ be a (compactly supported) distribution on $\mathbb R^n$ such that $\nabla u\in L^p$ for some $p\in (0,1)$. Does that imply some regularity for $u$? Note that in the case $p=1$, we get $u\in L^{n/(n-1)}$.