Riesz transforms for laguerre expansions

We analyze boundedness properties of some operators related to the heat-diffusion semigroup associated to Laguerre functions systems. In particular, for any α > -1, we introduce appropriate Laguerre Riesz Transforms and we obtain power-weighted V inequalities, 1 < p < ∞. We achieve this res...

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Detalles Bibliográficos
Autores: Harboure, Eleonor Ofelia, Torrea Hernández, José Luis, Viviani, Beatriz Eleonora
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2006
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/84074
Acceso en línea:http://hdl.handle.net/11336/84074
Access Level:acceso abierto
Palabra clave:Laguerre Functions Systems
Riesz Transforms
Weighted Inequalities
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descripción
Sumario:We analyze boundedness properties of some operators related to the heat-diffusion semigroup associated to Laguerre functions systems. In particular, for any α > -1, we introduce appropriate Laguerre Riesz Transforms and we obtain power-weighted V inequalities, 1 < p < ∞. 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 α = n/2 - 1. Such connection allows us to transfer known boundedness properties for Hermite operators to Laguerre operators corresponding to those specific values of α. To extend the results to any α > -1, we make use of transplantation and some weighted inequalities we obtain in the Hermite setting (which we believe of independent interest).