Compactness for the (partial derivative)over-bar-Neumann problem: a functional analysis approach

We characterize compactness of the (partial derivative) over bar -Neumann operator for a smoothly bounded pseudoconvex domain and in the setting of weighted L-2-spaces on 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 (partial derivative) over bar -Neumann operator on a smoothly bounded pseudoconvex domain.