Plemelj projection operators over domain manifolds (Q2718021)

The author introduces so-called domain manifolds, which are compact \(n\)-dimensional manifolds lying in \(\mathbb{C}\) with some special properties. It is proved the decomposition NEWLINE\[NEWLINEL^2(M)= H^2(M^+) \oplus H^2(M^-)NEWLINE\]NEWLINE where \(M\) is such a domain manifold and \(H^2(M^\pm)\) are corresponding Hardy spaces. Using techniques from both real and complex Clifford analysis analogue of the Kerzman-Stein kernel and Szegő projection operators are introduced and their properties studied.