Sharp subelliptic estimates for \(n-1\) forms on finite type domains (Q1347347)

Let \(\Omega = \{z: \;r(z)<0 \}\) be a smooth domain in \(\mathbb C^n\), \(x_0\in b\Omega\), and \(L\in T^{0,1}(b\Omega)\). Let \(R(L,x_0)=2+\min \{ m: (\Re (aL))^m \lambda_L (x_0) \neq 0\) for some \(\mathcal C^{\infty}\) function \(a\) near \(x_0 \},\) where \(\lambda_L\) denotes the Levi fom. It is assumed that there exists a vector field \(L\in T^{0,1}(b\Omega)\) with (i) \(\lambda_L=\partial \overline \partial r (L,\overline L)\geq 0,\) (ii) \(R(L,x_0)=m.\) The author shows that under these assumptions a subelliptic estimate of order \(\varepsilon =1/m\) holds at \(x_0\) for \((p,n-1)\) forms. It should be pointed out that it is not assumed that \(\Omega \) is pseudoconvex.