International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 4, Pages 98145, 19 p.
doi:10.1155/IJMMS/2006/98145
Generalized multidimensional Hilbert transforms in Clifford analysis
Fred Brackx
, Bram De Knock
and Hennie De Schepper
Clifford Research Group, Department of Mathematical Analysis, Faculty of Engineering, Ghent University, Gent 9000, Belgium
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.