The Hilbert Transform on the Unit Sphere in ℝm

  • F. Brackx
  • H. De Schepper
Conference paper
Part of the Trends in Mathematics book series (TM)


As an intrinsically multidimensional function theory, Clifford analysis offers a framework which is particularly suited for the integrated treatment of higher-dimensional phenomena. In this paper a detailed account is given of results connected to the Hilbert transform on the unit sphere in Euclidean space and some of its related concepts, such as Hardy spaces and the Cauchy integral, in a Clifford analysis context.


Hilbert transform Hardy space Cauchy integral 

Mathematics Subject Classification (2000)

Primary 30G35 Secondary 44A15 


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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2008

Authors and Affiliations

  • F. Brackx
    • 1
  • H. De Schepper
    • 1
  1. 1.Clifford Research Group Faculty of EngineeringGhent UniversityGentBelgium

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