Abstract
We collect and extend results on the limit of $\sigma^{1-k}(1-\sigma)^{k}|v|_{l+\sigma,p,\varOmega}^p$ as $\sigma\to0^{+}$ or $\sigma\to1^{-}$, where $\varOmega$ is $\mathbb{R}^n$ or a smooth bounded domain, $k\in\{0,1\}$, $l\in\mathbb{N}$, $p
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