Generalized multidimensional Hilbert transforms in Clifford analysis

Fred Brackx, Bram De Knock and Hennie De Schepper

International Journal of Mathematics and Mathematical Sciences, 2006, vol. 2006, 1-19

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 L 2 -functions.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:098145

DOI: 10.1155/IJMMS/2006/98145

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