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. © 2011 Elsevier Inc. All rights reserved