$$D^\alpha = T_{\alpha,|\alpha|} +T_{\alpha,|\alpha|-1}N+\cdots
+\nu^\alpha N^{|\alpha|},$$ where $T_{\alpha,k}$ is a tangential operator of order $\le k$, and $\nu:=$ $(\nu_1,\dots,\nu_{2n})$. Therefore the left hand side of (\[\*\]) equals $$\begin{aligned}
\lefteqn{
\sum_{i=0}^{s-1} \sum_{|\alpha|\le i} \CP \int_{b\Omega} \bigl( 
T_{\alpha,|\alpha|}+T_{\alpha,|\alpha|-1}N+\cdots+\nu^\alpha
N^{|\alpha|} \bigr)\phi_J} \\
& \qquad \qquad \cdot\overline{N D^\alpha (-\Delta)^{s-1-i}
(\K\psi)_J }\notag \\
& = \sum_{\ell=0}^{s-1} \biggl( \int_{b\Omega} 
N^\ell \phi_J \cdot \overline{ \bigl[ \sum_{i=\ell}^{s-1} 
\sum_{\ell\le|\alpha|\le i} \CP T_{\alpha,|\alpha|-\ell}^* 
ND^\alpha (-\Delta)^{s-1-i} (\K\psi)_J \bigr]} \biggr) \notag\\
& = \sum_{\ell=0}^{s-1} \biggl( \int_{b\Omega} 
N^\ell \phi_J \cdot \overline{ \sum_{\ell\le|\alpha|\le s-1} 
\bigl[ \sum_{j=0}^{s-1-|\alpha|} \CP T_{\alpha,|\alpha|-\ell}^* 
ND^\alpha (-\Delta)^{j} (\K\psi)_J \bigr]} \biggr) .
\label
{DAG} \end{aligned}$$ Notice that in the above calculations we have obtained the identity $$\begin{gathered}
\label{K-identity}
\la\phi,\K\psi\ra_s = \sum_J \biggl( \la\phi_J, 
\sum_{j=0}^{s}  (-\Delta)^j (\K\psi)_J \ra_0 \\
+ \sum_{\ell=0}^{s-1}  \int_{b\Omega} 
N^\ell \phi_J \cdot \overline{ \sum_{\ell\le|\alpha|\le s-1} 
\bigl[ \sum_{j=0}^{s-1-|\alpha|} \CP T_{\alpha,|\alpha|-\ell}^* 
ND^\alpha (-\Delta)^{j} (\K\psi)_J \bigr]} \biggr) .\end{gathered}$$ In particular, for $\nu:=$ $(\nu_1,\dots,\nu_{2n})$, we have that $T_{\alpha,0}=\nu^\alpha=T_{\alpha,0}^*$ and for $\ell$ a positive integer we have $$\label{***}
\sum_{|\alpha|=\ell-1}\CP \nu^\alpha D^\alpha=
\sum_{|\beta|=\ell-2}\CPb \nu^\beta \bigl(\sum_{i=1}^{2n}\nu_i
D_i\bigr)D^\beta=\dots= N^{\ell-1}.$$ Thus the last summand on the right hand side of (\[DAG\]) (corresponding to $\ell=s-1$) becomes $$\int_{b\Omega} N^{s-1} \phi_J\cdot \overline{\biggl(
\sum_{|\alpha|=s-1} \CP
T_{\alpha,0}^* \bigl[ ND^\alpha (\K \psi)_J \bigr] \biggr)} 
= \int_{b\Omega} N^{s-1} \phi_J\cdot \overline{N^s (\K\psi)_J} .$$ The right hand side 