Arkiv för Matematik

  • Ark. Mat.
  • Volume 46, Number 2 (2008), 285-313.

Power weighted Lp-inequalities for Laguerre–Riesz transforms

Eleonor Harboure, Carlos Segovia, José L. Torrea, and Beatriz Viviani

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In this paper we give a complete description of the power weighted inequalities, of strong, weak and restricted weak type for the pair of Riesz transforms associated with the Laguerre function system $\{\mathcal{L}_k^{\alpha}\}$, for any given α>-1. We achieve these results by a careful estimate of the kernels: near the diagonal we show that they are local Calderón–Zygmund operators while in the complement they are majorized by Hardy type operators and the maximal heat-diffusion operator. We also show that in all the cases our results are sharp.

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Ark. Mat., Volume 46, Number 2 (2008), 285-313.

Received: 15 December 2006
Revised: 20 April 2007
First available in Project Euclid: 31 January 2017

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2008 © Institut Mittag-Leffler


Harboure, Eleonor; Segovia, Carlos; Torrea, José L.; Viviani, Beatriz. Power weighted L p -inequalities for Laguerre–Riesz transforms. Ark. Mat. 46 (2008), no. 2, 285--313. doi:10.1007/s11512-007-0052-y.

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