On higher order Morrey's inequalities over RCD{\boldmath$(K,N)$}-spaces

In this paper, we establish a higher order Morrey’s inequality in the framework of %non-collapsed $\mathsf{R}\mathsf{C}\mathsf{D}(K,N)$-spaces for $K\in \mathbb{R}$ and $N\in \mathbb{N}$. We do so by first introducing an alternate version of the second order Sobolev space $W^{2,p}(X)$, which contains amply many functions even when $p>N$.