Precise subelliptic estimates for a class of special domains

For the -Neumann problem on a regular coordinate domain Ω ⊂ ℂ n +1 , we prove ∈ -subelliptic estimates for an index ∈ ≥ (2 m ) −1 , where m is the “multiplicity”. We also intend to supply here a much simplified proof of the existing literature. Our approach is founded on the method by Catlin in [2] , which consists of constructing a bounded family of weights {φ δ } whose Levi form is bigger than δ -2∊ on the δ -strip around ∂ Ω.