IMAL   13325
INSTITUTO DE MATEMATICA APLICADA DEL LITORAL "DRA. ELEONOR HARBOURE"
Unidad Ejecutora - UE
artículos
Título:
RIESZ TRANSFORMS FOR LAGUERRE EXPANSIONS
Autor/es:
E. HARBOURE, J. L. TORREA AND B. VIVIANI
Revista:
INDIANA UNIVERSITY MATHEMATICS JOURNAL
Referencias:
Año: 2006 vol. 55 p. 999 - 1014
ISSN:
0022-2518
Resumen:
We analyze boundedness properties of some operators related to the heat-diffusion semigroup associated to Laguerre functions systems. In particular, for any alpha > -1, we introduce appropriate Laguerre Riesz Transforms and we obtain power-weighted Lp inequalities, 1 < p < infinity. We achieve this result by taking advantage of the existing classical relationship between n-variable Hermite polynomials and Laguerre polynomials on the half line of type alpha = (n/2)-1. Such connection allows us to transfer known boundedness properties for Hermite operators to Laguerre operators corresponding to those specific values of alpha. To extend the results to any alpha > -1, we make use of transplantation and of ome weighted inequalities we obtained in the Hermite setting, which we beleive are of independent interest.