Resumen de Compactness for the ∂ -Neumann problem: a functional analysis approach

Friedrich Haslinger

• We characterize compactness of the {\overline{\partial}}-Neumann operator for a smoothly bounded pseudoconvex domain and in the setting of weighted L^2-spaces on {\mathbb{C}^n}. For this purpose we use a description of relatively compact subsets of L^2-spaces. We also point out how to use this method to show that property (P) implies compactness for the {\overline{\partial}}-Neumann operator on a smoothly bounded pseudoconvex domain.