  Let $\Omega$ be a pseudoconvex domain in $\mathbb C^n$ with smooth boundary
$b\Omega$. We define general estimates $(f\text{-}\mathcal M)^k_{\Omega}$ and
$(f\text{-}\mathcal M)^k_{b\Omega}$ on $k$-forms for the complex Laplacian
$\Box$ on $\Omega$ and the Kohn-Laplacian $\Box_b$ on $b\Omega$. For $1\le k\le
n-2$, we show that $(f\text{-}\mathcal M)^k_{b\Omega}$ holds if and only if
$(f\text{-}\mathcal M)^k_{\Omega}$ and $(f\text{-}\mathcal M)^{n-k-1}_{\Omega}$
hold. Our proof relies on Kohn's method in [Ann. of Math. (2), 156(1):213--248,
2002].
