On some properties of the Hilbert transform in Euclidean space
Delanghe, R.
Bull. Belg. Math. Soc. Simon Stevin, Tome 11 (2004) no. 1, p. 163-180 / Harvested from Project Euclid
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First some properties are recalled of the Hilbert transform introduced in the 1990's within the framework of Clifford analysis. Furthermore algebraic and geometric characterizations are given for this operator to be unitary. Special attention is paid to the Hilbert transform on the unit sphere $S^m$ and the hyperplane $\mathbb R^m$ in $\mathbb R^{m+1}$ and classical results in the plane are revisited.
Publié le : 2004-06-14
Classification:  Clifford analysis,  $H^p$-spaces,  Hilbert transform,  30G35,  42B30,  44A15 
@article{1086969309,
     author = {Delanghe, R.},
     title = {On some properties of the Hilbert transform in Euclidean space},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {11},
     number = {1},
     year = {2004},
     pages = { 163-180},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1086969309}
}

Delanghe, R. On some properties of the Hilbert transform in Euclidean space. Bull. Belg. Math. Soc. Simon Stevin, Tome 11 (2004) no. 1, pp.  163-180. http://gdmltest.u-ga.fr/item/1086969309/