Fix an integer $r\ge 0$. Let $T$ be an ordered extended knot vector on $[a,b]$ with no knot multiplicity exceeding $r+1$, and let $\{N_{i,r}: [a,b]\to [0,\infty)\}_{i\in\mathcal I}$ be the full finite normalized degree $r$ B-spline basis associated with $T$. For every coefficient family $(c_i)_{i\in\mathcal I}\subset\mathbb R$, define the spline $s: [a,b]\to\mathbb R$ by

\begin{align*} s(x)=\sum_{i\in\mathcal I} c_i N_{i,r}(x). \end{align*}

There exist constants $A_r,B_r>0$ depending only on $r$ such that

\begin{align*} A_r \max_{i\in\mathcal I} |c_i| \le \|s\|_\infty \le B_r \max_{i\in\mathcal I} |c_i|. \end{align*}

The constants are independent of the locations and spacings of the knots.