Parole chiave

• complex analysis
• holomorphic function
• Siegel domain
• Bergman space

Abstract Goal of this talk is to present some recent progress in the theory of holomorphic function spaces on homogenous Siegel domains of Type II. These domains are unbounded realisation of the homogeneous bounded domains and include the tube domains over homogeneous cones as a particular case. We first describe the structure and geometrical properties of such domains. Second, we introduce some classes of holomorphic function spaces, including the weighted Bergman spaces, and describe their boundary behaviour. Finally, we concentrate on the boundedness of the Bergman projections, presenting some recent results and open problems. This talk is based on joint work with Mattia Calzi.