Regularity at the boundary and tangential regularity of solutions of the Cauchy-Riemann system (Q387730)

The authors consider, for a pseudoconvex domain, local regularity of \((\overline{\partial}, \overline{\partial}^{*})\) and of \((\overline{\partial}_{b}, \overline{\partial}_{b}^{*})\). They show that (pseudo)local regularity estimates on the boundary imply the analogous estimates in the interior. To go in the other direction, a stronger assumption is needed in the interior. The authors indicate a class of domains where this stronger assumption can be verified.NEWLINENEWLINEThe proof uses microlcal techniques and in particular an extension form the boundary that is well defined only in the positive part of the microlocalization (and so differs from Kohn's harmonic extension).