Power weighted$L$^{$p$}-inequalities for Laguerre–Riesz transforms

Eleonor Harboure IMAL-FIQ, CONICET, Universidad Nacional del Litoral Carlos Segovia Instituto Argentino de Matemática (IAM), CONICET, Saavedra 15, Ciudad Autónoma de Buenos Aires, Argentina José L. Torrea Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid Beatriz Viviani IMAL-FIQ, CONICET, Universidad Nacional del Litoral

TBD mathscidoc: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.
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  title={Power weighted$L$^{$p$}-inequalities for Laguerre–Riesz transforms},
  author={Eleonor Harboure, Carlos Segovia, José L. Torrea, and Beatriz Viviani},
  booktitle={Arkiv for Matematik},
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.
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