Compactness of the -Neumann operator on singular complex spaces

Let X be a Hermitian complex space of pure dimension n. We show that the -Neumann operator on (p,q)-forms is compact at isolated singularities of X if p+q≠n−1,n and q⩾1. The main step is the construction of compact solution operators for the -equation on such spaces which is based on a general characterization of compactness in function spaces on singular spaces, and that leads also to a criterion for compactness of more general Green operators on singular spaces.