Examples of non-semisimple Hopf algebra actions on Artin-Schelter regular algebras

Let $\mathbb{k}$ be a base field of characteristic $p>0$ and let $U$ be the restricted enveloping algebra of a 2-dimensional nonabelian restricted Lie algebra. We classify all inner-faithful $U$-actions on noetherian Koszul Artin-Schelter regular algebras of global dimension up to three.