Fredholm property of a family of operators on the five-dimensional Heisenberg group

An expansion in Euclidean spherical harmonics on the ball in the Heisenberg group of dimension five decomposes the Dirichlet problem for the Laplacian in an infinite number of two-dimensional problems. Fundamental solutions are obtained for each of the partial differential operators in these problems, thus reducing them further (via layer potentials) to one-dimensional integral equations. The main result in this article states that the corresponding integral operators are Fredholm in appropriate weighted L-2 spaces. (C) 2003 Elsevier Science (USA). All rights reserved.