International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 98145, 19 pages
doi:10.1155/IJMMS/2006/98145
Generalized multidimensional Hilbert transforms
in Clifford analysis
Clifford Research Group, Department of
Mathematical Analysis, Faculty of Engineering, Ghent
University, Gent 9000, Belgium
Received 26 September 2005; Accepted 29 December 2005
Copyright © 2006 Fred Brackx et al. 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
Two specific generalizations of the multidimensional Hilbert
transform in Clifford analysis are constructed. It is shown that
though in each of these generalizations some traditional
properties of the Hilbert transform are inevitably lost, new
bounded singular operators emerge on Hilbert or Sobolev spaces of
L2-functions.