Power weighted L inequalities for Laguerre Riesz Transforms

E. HARBOURE, C. SEGOVIA, J.L. TORREA Y B. VIVIVANI

ARKIV FOR MATEMATIK

Lugar: 46 (2008), 285-313.; Año: 2008 vol. 46 p. 285 - 313

0004-2080

In this article we give a complete description of the power weighted inequalities of stronng, weak and restricted weak type for a pair of Riesz transforms associated to a Laguerre system for any value of the parameter greater than -1. We achieve this result by a careful estimate of the kernels: 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 of the heat-diffusion operator. We also show that all our results are sharp.