Abstract
We construct a parametrix for the ∂ ̄ -Neumann problem on any pseudoconvex domain of finite type which reduces completely the study of (isotropic) L p -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 C 2 .
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