In the thirteen months covered by this report, the Experienced Researcher obtained several novel results, both in the expected directions indicated in the grant proposal, and in unexpected ones. The most notable outcomes of the project are: the discovery of a new extremality property of Lp operator norms of Szegő projections on abstract CR manifolds, in collaboration with B. Lamel (University of Vienna); a proof of L1 unboundedness of Bergman and Cauchy-Szegő projections in great generality; new pointwise estimates for Bergman kernels under appropriate geometric conditions, in collaboration with D. N. Son (University of Vienna); the development of a method to study Bergman projections on domains containing complex manifolds in their boundary; the introduction of a new transfinite construction in several complex variables related to the Diederich-Fornæss index, in collaboration with S. Mongodi (Politecnico di Milano); a new sharp multiplier theorem of Mihlin-Hörmander type for two-dimensional Grushin operators, in collaboration with the Supervisor A. Martini.
Moreover, the researcher visited several European research institutions (University of Vienna, Centre de Recerca Matematica in Barcelona, Istituto Nazionale di Alta Matematica in Rome, Isaac Newton Institute in Cambridge, Politecnico di Milano, Università degli Studi di Milano Statale, Università di Milano-Bicocca), gave in-presence and virtual research seminars, and helped organize seminars at the Host institution.
