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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Abstract

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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485907077

Digital Object Identifier
doi:10.1007/s11512-007-0062-9

Mathematical Reviews number (MathSciNet)
MR2529705

Zentralblatt MATH identifier
1187.42003

Rights
2008 © Institut Mittag-Leffler

Citation

Kobayashi, Toshiyuki; Nilsson, Andreas. Indefinite higher Riesz transforms. Ark. Mat. 47 (2009), no. 2, 331--344. doi:10.1007/s11512-007-0062-9. https://projecteuclid.org/euclid.afm/1485907077


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