الفهرس 
Chapter I: PreliminariesOnly 14 pages are availabe for public view
 |  | from | 126 |  |  |
| | | from | 126 | | |
Abstract
In this thesis, on a bounded strongly pseudo-convex domain in Cn with piecewise smooth boundary (resp. with Lipschitz boundary), we prove that the @-Neumann operator N is bounded from Sobolev (¡1=2)-space to the Sobolev (1=2)-space. Furthermore, we prove that the operators N, @N and @ ¤ N are compact on the Sobolev (¡1=2)-space. We obtain L2-existence theorems for the @-problem and hence for the @-Neumann problem on a strongly q-convex (resp. Hartogs pseudo-convex) domain in a KÄahler manifold. Finally, we obtain a solution to the @-equation with exact support in a domain with non-smooth boundary in a complex manifold X. This is done for complex-valued forms of type (r; s), s ¸ 1, on a domain with boundary satisfying Property B. Furthermore, we solve this equation for forms of type (r; s), q · s · n ¡ q, with values in a holomorphic vector bundle when the domain is strongly q-convex.