Exact regularity of Bergman, Szegö and Sobolev space projections in non pseudoconvex domains
Let \(\Omega\) be a smooth, bounded Reinhard domain. It is shown that the Bergman and the Szegö projections, as well as the higher order Sobolev space analogues of the Bergman projection, all satisfy exact regularity estimates in Sobolev norms. These estimates were previously known only under the additional assumptions of pseudoconvexity and completeness of \(\Omega\). For the case of the Bergman projection, it is shown that exact regularity is actually true more generally on domains with ''transverse symmetries''.
higher order Sobolev space analogues of the Bergman projection
scientific article; zbMATH DE number 3914979
scientific article