T. Kobayashi and A. Nilsson,
Indefinite higher Riesz transforms,
Arkiv för Matematik 47 (2009), 331-344. (published online first, on 3 March 2008)..

Stein's higher Riesz transforms are translation invariant operators on L2(Rn) built from multipliers whose restrictions to the unit sphere are eigenfunctions of the Laplace-Beltrami operators. In this article, generalizing Stein's higher Riesz transforms, we construct a family of translation invariant operators by using discrete series representations for hyperboloids associated to the inde nite quadratic form of signature (p,q). We prove that these operators extend to Lr-bounded operators for 1 < r < if the parameter of discrete series representations is generic.

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The original publication is available at www.springerlink.com.

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