Plemelj projection operators over domain manifolds

Plemelj projection operators are introduced for spaces of square integrable functions defined over the boundaries of a class of compact real n-dimensi onal manifolds lying in C-n. These manifolds possess many properties simila r to domains in IRn, and are consequently called domain manifolds. The key ingredients used here are techniques from both real and complex Clifford an alysis. Analogues of the Kerzman-Stein kernel and Szego projection operator s are introduced, and their conformal covariance is described.