Inheritance of noncompactness of the ¯∂ -Neumann problem

In this paper we show that noncompactness of the ¯∂ -Neumann operator on a smooth, bounded, pseudoconvex Reinhardt domain Ω in C2 implies noncompactness of the ¯∂ -Neumann operator of higher-dimensional domains fibered over Ω under a suitable size restriction on the fibers.  2004 Elsevier Inc. All rights reserved