A sufficient condition for subellipticity of the ¯∂-Neumann operator

We give a sufficient condition for subelliptic estimates for the ¯∂-Neumann operator on smoothly bounded, pseudoconvex domains in Cn. This condition is a quantified version of McNeal’s condition (P˜) for compactness of the ¯∂-Neumann operator, and it extends Catlin’s sufficiency condition for subellipticity as it is less stringent. © 2006 Elsevier Inc. All rights reserved