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

Friedrich Haslinger

• We characterize compactness of the ∂ -Neumann operator for a smoothly bounded pseudoconvex domain and in the setting of weighted L 2-spaces on ℂ? . 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 ∂ -Neumann operator on a smoothly bounded pseudoconvex domain.