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-dimensional manifolds lying in C. These manifolds posses many properties similar to domains in R, and are consequently called domain manifolds. The key ingredients used here are techniques from both real and complex Clifford analysis. Analogues of the Kerzman-Stein kernel and Szegö projection operators are introduced, and their conformal covariance is described.