International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 10, Pages 613-624
doi:10.1155/S0161171202011870
Szegö projections for Hardy spaces of monogenic functions and applications
Swanhild Bernstein1
and Loredana Lanzani2
1Institute of Mathematics and Physics, Bauhaus-Universität Weimar, Coudraystr. 13b, Weimar 99421, Germany
2Department of Mathematics, The University of Arkansas at Fayetteville, Fayetteville 72701, AR, USA
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.