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...
| Autores: | , , |
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| 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 |
| 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). |
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