\begin{align}
\Vert \pi_{k+1}(f)-\pi_{k}(f)\Vert_{n}&\le\sqrt{u}2^{k/2}\frac{[2(1+\sqrt{2})+1]^{1/2}}{\sqrt{n}}\Vert\pi_{k+1}(f)-\pi_{k}(f)\Vert_{\psi_2},\\
\Vert \Pi_{k+1}(g)-\Pi_{k}(g)\Vert_{n}&\le\sqrt{u}2^{k/2}\frac{[2(1+\sqrt{2})+1]^{1/2}}{\sqrt{n}}\Vert\Pi_{k+1}(g)-\Pi_{k}(g)\Vert_{\psi_2}.\label{thm:product:process:eq2}
\end{align}
