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If $P$ is a degree $ l $ differential operator, then
$ |Pu||_s < C || u ||_{s+l}$ , $\forall u, s. $$$ \Vert Pu \Vert_s < C \Vert u \Vert_{s+l} ,\;\; \forall u, s. $$
Now take $s=-k$, $P=\nabla^l$. (Sorry. There seems to ne a problem with MathJaxs
If $P$ is a degree $ l $ differential operator then
$ |Pu||_s < C || u ||_{s+l}$ , $\forall u, s. $
$$ \Vert Pu \Vert_s < C \Vert u \Vert_{s+l} ,\;\; \forall u, s. $$
Now take $s=-k$, $P=\nabla^l$.
If $P$ is a degree $\ell$$ l $ differential operator then
$$\|Pu\|_s\leq C\|u\|_{s+\ell},\;\;\forall u, s$$$ |Pu||_s < C || u ||_{s+l}$ , $\forall u, s. $
Now take $s=-k$, $P=\nabla^\ell$$P=\nabla^l$. (Sorry. There seems to ne a problem with MathJaxs
If $P$ is a degree $\ell$ differential operator then
$$\|Pu\|_s\leq C\|u\|_{s+\ell},\;\;\forall u, s$$
Now take $s=-k$, $P=\nabla^\ell$.
