# MathSciDoc: An Archive for Mathematician ∫

#### TBDmathscidoc:1701.333127

Arkiv for Matematik, 46, (2), 285-313, 2006.12
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.
@inproceedings{eleonor2006power,
title={Power weighted$L$^{$p$}-inequalities for Laguerre–Riesz transforms},
author={Eleonor Harboure, Carlos Segovia, José L. Torrea, and Beatriz Viviani},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203622345936936},
booktitle={Arkiv for Matematik},
volume={46},
number={2},
pages={285-313},
year={2006},
}

Eleonor Harboure, Carlos Segovia, José L. Torrea, and Beatriz Viviani. Power weighted$L$^{$p$}-inequalities for Laguerre–Riesz transforms. 2006. Vol. 46. In Arkiv for Matematik. pp.285-313. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203622345936936.