Generalized multidimensional Hilbert transforms
in Clifford analysis

Brackx, Fred; De Knock, Bram; De Schepper, Hennie

doi:https://doi.org/10.1155/IJMMS/2006/98145

International Journal of Mathematics and Mathematical Sciences

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Volume 2006 | Article ID 098145 | https://doi.org/10.1155/IJMMS/2006/98145

Generalized multidimensional Hilbert transforms in Clifford analysis

Fred Brackx,¹Bram De Knock,¹and Hennie De Schepper¹

Received26 Sept 2005

Accepted29 Dec 2005

Published01 Jun 2006

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.

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Copyright © 2006 Hindawi Publishing Corporation. 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.

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