Abstract
On a bounded q-pseudoconvex domain Omega in C-n with Lipschitz boundary b Omega, we prove the L-2 existence theorems of the <(partial derivative) over bar>(b)-operator on b Omega. This yields the closed range property of <(partial derivative) over bar>(b) and its adjoint <(partial derivative) over bar>(b)*. As an application, we establish the L-2-existence theorems and regularity theorems for the <(partial derivative) over bar>(b)-Neumann operator.