Solution operators for the \(\bar\partial\)-equation on non-transversal intersections of strictly pseudoconvex domains (Q1191411)

Solution operators for the inhomogeneous Cauchy-Riemann equation on non- transversal intersections of strictly pseudoconvex domains are constructed. We consider arbitrary intersections of three domains, \(D=D'\cap\Omega\cap D''\), where \(D'\) and \(D''\) are strictly pseudoconvex domains with not necessarily smooth boundary and \(\Omega\) is a transversal intersection of finitely many strictly pseudoconvex domains with smooth boundaries. For such domains we construct operators with uniform estimates and operators which map the \(C^{2k}\)-forms on \(\overline D\) which admit extensions to \(C^{2k}\)-forms on a neighbourhood of \(\overline D\), continuously into the space of \(C^k\)-forms on \(\overline D\). It is not clear whether one can avoid this loss of regularity or not.