Maximal hypoellipticity for the ∂¯-Neumann problem

We establish maximal hypoellipticity for the ∂¯-Neumann problem on smooth, bounded pseudoconvex domains in CnCn under the weakest possible condition on the Levi form. In particular, maximal hypoellipticity holds on the level of (n−1)(n−1)-forms for pseudoconvex domains of finite commutator type.