International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 10, Pages 613-624
doi:10.1155/S0161171202011870

Szegő 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

Received 6 February 2001; Revised 12 June 2001

Copyright © 2002 Swanhild Bernstein and Loredana Lanzani. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.