Arkiv för Matematik

  • Ark. Mat.
  • Volume 47, Number 2 (2009), 331-344.

Indefinite higher Riesz transforms

Toshiyuki Kobayashi and Andreas Nilsson

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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 indefinite quadratic form of signature (p, q). We prove that these operators extend to Lr-bounded operators for 1< r<∞ if the parameter of the discrete series representations is generic.

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Ark. Mat., Volume 47, Number 2 (2009), 331-344.

Received: 2 April 2007
First available in Project Euclid: 31 January 2017

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2008 © Institut Mittag-Leffler


Kobayashi, Toshiyuki; Nilsson, Andreas. Indefinite higher Riesz transforms. Ark. Mat. 47 (2009), no. 2, 331--344. doi:10.1007/s11512-007-0062-9.

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