Derivative supremum norm
= Derivative supremum norm
{title2=$|u|_{k;U}$}
For a function with bounded derivatives through order $k$, the derivative <supremum norm> is $|u|_{k;U}=\sum_{j=0}^k\sup_U|D^j u|$, with any equivalent finite-dimensional norm for each derivative tensor. This is a classical $C^k$ norm; it is different from the <Lp norm> with exponent $k$.