Szegő projections for hardy spaces of monogenic functions and applications

Abstract

We introduce Szegő projections for Hardy spaces of monogenic functions defined on a bounded domain Ω in ℝn. We use such projections to obtain explicit orthogonal decompositions for L2(bΩ). As an application, we obtain an explicit representation of the solution of the Dirichlet problem for balls and half spaces with L2, Clifford algebra-valued, boundary datum.