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A Sobolev space is a vector space of functions equipped with a norm that is a combination of Lp-norms of the function itself and its derivatives up to a given order.
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Compact embeddings RKHSs into Sobolev Spaces
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 som …