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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Abstract

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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485907039

Digital Object Identifier
doi:10.1007/s11512-007-0052-y

Mathematical Reviews number (MathSciNet)
MR2430728

Zentralblatt MATH identifier
1161.44005

Rights
2008 © Institut Mittag-Leffler

Citation

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. https://projecteuclid.org/euclid.afm/1485907039


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