Sharp subelliptic estimates for $n-1$ forms on finite type domains

Abstract

Let $x_0\in b\Omega $ in a smooth domain $\Omega \subset \C^n$, which is not assumed to be pseudoconvex. We define a finite type condition $R( L,x_0) $ for a vector field $L\in T^{1,0}( b\Omega)$, which equals the well-known type $c(L,x_0) $ in certain important cases. We prove that if $R(L,x_0)=m$, then a subelliptic estimate of order $1/m$ holds at $x_0$ for $(p,n-1)$ forms.