Power weighted L inequalities for Laguerre Riesz Transforms

E. HARBOURE; C. SEGOVIA; J. L. TORREA; B. VIVIANI

ARKIV FOR MATEMATIK

Año: 2007

0004-2080

Abstract. In this paper we give a complete descripition for the power inequalities, of strong, weak and resticted weak type for the pair of Riesz transforms associate to the Laguerre function system {L(alpha,k)}, for any alpha > - 1.We archieve these results by a careful estimate of the kernel: near the diagonal we show that they are local Calderón-Zygmund 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