A parametrix for the ∂̄-Neumann problem on pseudoconvex domains of finite type

We construct a parametrix for the ∂̄-Neumann problem on any pseudoconvex domain of finite type which reduces completely the study of (isotropic) Lp-Sobolev and Hölder estimates to those for ∂̄b and □b. We also establish the “maximal” (nonisotropic) estimates in the case of D(q) domains and provide a precise comparison of the Bergman and Szegö projections (and of the canonical solutions to ∂̄ with respect to these two operators). The argument is substantially simpler than the known ones for the cases of strongly pseudoconvex domains and pseudoconvex domains of finite type in C2.