I am reading Elliptic operators with infinite-dimensional state spaces, Herber Amann. I am confuse with the norm of the space $BUC^s$ with $s\in \mathbb R_{+}$
For me i guess that $||u||_{BUC^s}=\sup_{[s]\geq k\geq 1}||D^{k}u||_{L_{\infty}}=\sup_{[s]\geq k\geq 1}\sup_{\text{Domain of}\quad u}|D^{k}u|$ am I interpretating in the correct way?
$[s]$ is the largest integer less or equal to $s$.
Thanks for hints or references