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Let $m\in \mathbb{N}$, $p\in [1,\infty]$, $W^{m,p}([0,1])$ the space of all functions $[0,1]\rightarrow \mathbb{R}$ which are $m$ times weakly differentiable and weak derivatives in $L^p$, $$|u|_{W^{...

Suppose that $f : [0, 1] \to \mathbb{R}$ is an element of the order-$k$ Sobolev space, \begin{multline} f^{(k - 1)}~\text{is absolutely continuous},\quad \|f\|_{W^k}^2 := \int_0^1 f^{(k)}(x)^2 \, dx &...