Plemelj Projection Operators over Domain Manifolds
arXiv:math/9805038
Abstract
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^n. These manifolds posses many properties similar to domains in R^n, 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 Szego projection operators ar introduced, and their conformal covariance is described.
16 pages e-mail address: [email protected] Key words: Dirac operators, singular integral operators, Hardy spaces, Plemelj operators, Clifford algebras