Sobolev derivative estimate
= Sobolev derivative estimate
For every multi-index $\alpha$ and real $s$,
$$
\|D^\alpha u\|_{H^{s-|\alpha|}}
\leq\|u\|_{H^s}.
$$
This follows from the Fourier multiplier $(i\xi)^\alpha$.
= Sobolev derivative estimate
For every multi-index $\alpha$ and real $s$,
$$
\|D^\alpha u\|_{H^{s-|\alpha|}}
\leq\|u\|_{H^s}.
$$
This follows from the Fourier multiplier $(i\xi)^\alpha$.