Comparaison des projecteurs de Bergman et Szegö et applications. (Comparison of the Bergman and Szegö projectors, and applications)
Denote by B and S the Bergman and Szegö projections, respectively, associated to a bounded domain D in \({\mathbb{C}}^ n\). When comparing solutions to the \({\bar \partial}\)-equation minimizing \({\mathcal L}^ 2\)- norms over bD and over D, respectively, one is led to compare S-B. In the paper under review, the author considers strictly pseudoconvex domains and gives \({\mathcal L}^ p\)-type estimates \((1<p)\) for Su-Bu in terms of \({\bar \partial}u\). The method is to use the known asymptotic expansions of S and B, and to exhibit the principal part of S-B as an explicit integral operator. An application to \({\mathcal L}^ p(bD)\)-estimates for the canonical solution u-Bu to \({\bar \partial}u=f\) is also given.
scientific article; zbMATH DE number 4146386
scientific article