Estimates for the solution of \(\overline\partial\) on an intersection of strictly pseudoconvex open sets
Using Berndtsson and Andersson kernels, we obtain a solution of the equation \(\overline \partial u=w\) for \(w\) defined on a transversal intersection of strictly pseudoconvex domains. The solution is given by an integral supported only by the domain \(\Omega\) considered. This allow us to have, in particular, \(u\) in \(L^p_{(0,q-1)} (\Omega)\) for \(w\) in \(L^p_{(0,q)} (\Omega)\).
scientific article; zbMATH DE number 1028176