Compact embeddings RKHSs into Sobolev Spaces

Question

Let $\mathcal{H}$ be an RKHS over an open domain $\Omega \subseteq \mathbb{R}^d$. Are there conditions under which $\mathcal{H}$ can be compactly embedded in a Sobolev space $W^{s,p}(\Omega)$ for some $s\in \mathbb{R}$ and $p\in [1,\infty]$. Equally importantly, in such cases, do we have estimates on $s$ and $p$ in terms of some data/properties of $\mathcal{H}$.